Mobile Safari plays MPEG4/H.264 using HTML5 in Safari, Mobile Safari and what ever you want to call Safari on the iPad. It does not play the OGG version that Firefox does.
MPEG4/H.264 will probably be the one that wins because its the one the big players are putting there weight behind.
Unfortunately, it is extremely unlikely that the Mozilla Foundation will be at liberty to directly ship a version of Firefox that natively supports H.264 within the next decade or so due to patent restrictions, unless the MPEG LA agrees to an open-source exemption (or something to the same effect) for viewers.
Even if they had the financial resources to purchase a license for every copy of Firefox that is downloaded directly from them, the browser's license terms state that anybody else can redistribute the software they received to others as well. Somebody would also need to pay the patent royalties for those additional copies, and any copies of the copies, etc.
This is the reason Google distributes the H.264 codec as part of its proprietary (non-redistributable) Chrome browser, but does not include it as part of its redistributable open source Chromium counterpart. And Apple distributes the H.264 as part of Safari, but excludes it from the redistributable WebKit.
So if H.264 wins out, judging by current usage statistics, there will be a significant share of web browsers that can claim to be fully HTML5 compliant, but still the market will be fragmented.
From what I'd read, the W3C's policy is that it should be possible to implement their baseline standards on a royalty-free basis, so it seems almost certain to me that H.264 codec support will not be called up as a mandatory component of HTML5.
They had originally specified OGG Theora as a mandatory codec, but at Apple's insistence (ironically, due to Apple's alleged uncertainty about OGG Theora's patent situation), they removed it. They intentionally did not replace it with H.264 due to other W3C members' objections to H.264's patent requirements that have already been positively identified, so they left the codec undefined. If anything, they will probably leave it undefined and allow the the individual web browser developer to decide on a case-by-case basis. So we could see a fully certified HTML5 compliant version of Microsoft IE 10 that only plays back WMV files.