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Some of the very basic tests I once did show them (MSVC 9.0/Visual Studio 2008 and GCC 4.5-odd) running pretty much neck and neck, without much real advantage to either one or the other. It really comes down to compiler, code and the specific optimization flags one uses. Otherwise, they're both pretty much the same.

Here's someone else's benchmark, showing GCC and MSVC just about the same, and Intel's ICC about 20% or more faster. By your logic, ICC should be the world's favourite compiler, since it's a) the fastest, and b) available on all platforms.

The real world doesn't work like that, though - ICC has other problems...

The difference is 20% compared to baseline profile at relatively high bitrates. The iphone 3gs, iphone 4, ipad and newer ipod touch model support high profile fine and then the difference is closer to 100%.

The analysis on the x264 blog concluded that VP8 most closely resembles H.264 baseline, and the comparison shows that H.264 baseline encoded with x264 lies somewhere between Theora and H.264 Main.

The Xbox graphics chipset had only two advantages over PC chipsets of the time: 3D graphics, and SDTV output as a standard feature. The SDTV feature is less important now that virtually all TVs made in the past three years have VGA and HDMI inputs. And unless one writes half the video decoder in a shader (as in some modern H.264 decoders), 3D graphics won't take much load off the CPU for video decoding; perhaps the biggest thing a GeForce 3-class pixel shader can do is help convert YUV to RGB. Remember that the video codec that was popular among pirates and spaceshifters at the time was MPEG-4 Advanced Simple Profile (DivX and Xvid), which is roughly on par with Theora and less computationally complex than H.264.

for a fair comparison you need to know the data spent for equal quality, and I don't think you know that here

This comparison shows that Xvid, x264 at H.264 Baseline Profile, and Theora are all fairly close, but x264 Main Profile needs about half the data for a given quality.

There are many reasons why this is not happening, so this is going to be pretty long.

More than 60% of the video on the web today is H.264 and the percentage is growing. Wide deployment of the codec has started in 2007 when Adobe added it to Flash and the iPhone was released prompting Youtube to convert all its video to H.264. Two years later, when it was already the dominant format and after it had already been dropped as a required format for HTML5, the Xiph guys came along with the first halfway decent release of Theora (1.1) and expected everyone to change what they had been doing for the last couple of years.
By then H.264 had already become somewhat a de facto standard for video on the web and had wide support in software and hardware, especially mobile phones and home media centers. Since everyone already been pushing for H.264, the licensing fees for the encoders/decoders were cheap and there are no fees on free web video no one had an incentive to reencode all their content to a technically inferior format with way less compatibility to existing hardware and software. For the video providers there is no savings. If anything they'd need to spend extra money to reencode and they'd need more storage/bandwith to provide the same quality in Theora.

The state of the Theora encoder and the technical inferiority of the format is also a hindrance to adoption.
Currently H.264 encoding on Youtube is done by x264, an open source encoder that is also used by other companies (Facebook, Criterion,...) who also sponsor development of certain features. x264 is one of the best H.264 encoders around, is highly configurable and can provide high speed and quality. Gregory Maxwell, one of the Theora developers, posted in a comparison that x264 contains more lines of handwritten assembly than the entire size of libtheoras C encoder codebase. So in its current state the Theora encoder is relatively slow for a format as simple as that.
Then there is the quality issue. If you compare metrics, Theora needs about 30% more bitrate than H.264 baseline profile and about 100% more bitrate than H.264 high profile to achieve the same quality. If you look at the actual subjective quality the situation is worse than that, although the current development version of Theora (1.2) should cut that by a couple of percent. Unfortunately when it comes to quality H.264 has more room to grow than Theora. While most video provided for cell phones today is H.264 baseline profile recent phones support High Profile (Nexus One, iPhone 3GS,...) and the share of available High Profile content is also growing.

Here is a more recent comparison in case you are interested. It looks at a film source. Criticism (see comments) includes the author not testing the Theora 1.2 alpha and using insanely slow x264 settings that more than double encoding time while giving less than 1% quality gain.

(mind that *all* other existing current codecs are inferior)

I'm starting to think this is becoming a "just repeat it often enough and everybody will believe it" case.

KeyJ's codec comparison shows that Theora needs twice the bits for the same subjective picture quality. How is that argumentum ad nauseam?

People don't get tired claiming this and everybody just parrots somebody who said it before.

You say parroting; I say citing a source. Can you cite a better source?

That the comparison linked by the gp is crap is one of the few things the developers of Theora and x264 can agree on.
Try this one . Check the comments for criticism by both the Theora and H.264 camp. Theora supporters complain that the Theora 1.2 alpha wasn't tested, H.264 supporters complain that settings more then doubling encoding time while gaining less than one percent quality were used.

tl;dr
Theora needs about 25% more bitrate than H.264 Baseline Profile and about twice the bitrate of H.264 High Profile to get the same metrics. If you look at the visual quality the situation is worse than that.

Financial objections? What, the price is too low?

You still have to pay people to implement Theora. You have to integrate it into players and browsers, if you offer Theora then you'll likely have to reencode,...

"Vastly"? How can you just make a sweeping claim like that without anything to back it up?

How about using google? There are countless comparisons pitting H.264 and Theora against each other. Basically Xiph says it's more or less on par and everyone else says it's vastly inferior. This comparison is pretty well done and easily reproducible: KeyJ comparison
There is some criticism. The Theora camp complains that the Theora 1.2 alpha version wasn't tested. The H.264 camp complains that insanely slow settings that more than doubled encoding time while giving less than 1% additional quality were used. If you go by metrics Theora needs about twice the bitrate of H.264 High Profile and around 25% more bitrate than H.264 Baseline Profile. If you take visual quality into account the situation looks worse for Theora.

I would say MPEG-2 is vastly inferior to MPEG-4; but Theora is somewhere in the middle.

Depends on the bitrate. For low bitrates Theora is about halfway between H.264 Baseline Profile and MPEG-2. As bitrates get higher MPEG-2 gains on Theora and they come out more or less the same. From the screenshots in the comparison I linked the 1000 kbps MPEG-2 screenshot looks better than the equivalent Theora screenshot. By they way if you read the comments in your bemasc.net link you'll see that there are also links to MPEG-2 beating Theora.

On the other hand, VP8 is supposed to be better than h.264.

This is purely marketing. No settings are given and only screenshots and a reencoded comparison video are available. Since VP8 has never been puplicly available there are no independent comparisons, so we'll have to wait for that until we can really determine how good it is.
From what I've seen VP8 should still be pretty good. It is basically VP7 adaped to be more easily implemented in hardware. I'd guess you could get better quality than H.264 Baseline Profile out of it. It can probably be improved in the future by optimizing the encoders. On2 own codec implementations are notorious smoothing the image too much during encoding thus killing details, a problem the Theora developers have addressed somwhat in their current work.

But I won't pass that judgment until I can see for myself.

You can easily test it yourself. Theora and x264 binaries are easy to find if you just google them.

And that isn't enough? [bemasc.net] Of course, we still have till 2016 to avert this disaster.

This would be the same disaster that only last year people said was inevitable in 2011. Given the MPEG-LAs history it's more likely that nothing will change in 2016.
You shoudn't be too surprised that people won't just switch over to Theora on a whim. If you take Youtube for instance they don't pay a cent for H.264 use so cost isn't a factor. (Although Google pays H.264 licensing fees for the decoder they ship with Chrome.) Switching to Theora would mean loss of wide compatibility, loss of quality or increase of filesizes, switching from a highly optimized and configurable (for speed or quality; speed in the case of Youtube) H.264 encoder, x264, to a slow, slighly buggy Theora encoder while gaining no business advantages.

On the other hand theora's main problem is not performance

True, Theora is noticeably better than H.263 and roughly on par with MPEG-4 Part 2, but H.264 needs half the bits of a Theora encode to show the same picture quality on live-action video.

is that it allows direct content downloading

That's not a codec issue. HTML5 using H.264 and HTML5 using Theora both expose a URL from which the user can download the video.

Video encoder comparison

Ogg Theora vs. H.264: head to head comparisons

Well the parent hasn't replied, so I will. Here is your first comparison to look at, and here is your second. Both found H.264 to be superior.

Oh, and here's some crow for you to snack on while you're reading.

Here, lets try something a little more scientific, shall we?

http://keyj.s2000.ws/?p=356

So before someone starts the whole "which codec is better" flamewar again: someone at xiph thinks theora is better, ars thinks h264 is better, and this guy has a do it yourself kit in the form of a shell script.

Have fun arguing, as the past few articles have been quite fruitful in that area. Sadly few have realized (despite it being the main focus of most of those articles, but hey, who reads those) that quality will not be the merit to win this battle.

DVD uses MPEG-2 video compression. This comparison shows that for standard-definition material, H.264 looks as good at 1 Mbps as MPEG-2 looks at 2 Mbps. This should compensate for the HD picture (1280x720) being over twice as big as DVD (704x480).

It is not significantly worse either.

Depends on what you call significant. In my personal experience Theora (1.1) needs between two and three times the bitrate (depending on content) of H.264 high profile (using a recent revision of x264) if you use the defaults in both encoders. If you limit the encoder to a single core the x264 encode will take ~30% longer. If you have a multicore CPU x264 will be faster since Theora isn't threaded. With H.264 baseline profile you'll only need between 50% and 100% more bitrate with Theora.

There is a recent comparison that's pretty good with pictures to back up my claims: http://keyj.s2000.ws/?p=356#more-356
You can find criticism in the comments section. It mainly concerns that the x264 settings used were insanely slow and that the Theora 1.2 alpha wasn't tested as well. I heard from people who tested it (doom9 forum) that currently Theora 1.2 often produces worse results than 1.1 since it is still in early stages of development.

h.264 has a deadline set for when free use ends. That deadline may or may not be pushed back and the royalties may or may not be extortionate.

No it doesn't. Every five or so years the MPEG-LA relicenses their whole patent pool, not just H.264. That's not the same as a deadline when free use ends.
It also doesn't really have an effect on private users since for most stuff fees only have to be payed if you do it for profit or distribute more than 100.000 units (encoders and decoders). For instance Youtube probably doesn't pay anything for an H.264 license since they don't meet any of the criteria. Google on the other hand pays licensing fees, probably the 5 million yearly cap, for the decoder the ship with Chrome since the exceed the 100k units. (Yes, I know that Google owns Youtube)

Check out this comparison. It's newer and in my opinion pretty good (apart from the speed part). Don't trust the metrics too much but rather look at the pictures.
The author is probably going to do another one with input from the codec developers.