What is the involvement of each company in open source drivers ?
- Nvidia - none.
- ATI/AMD - they make OSS drivers for their cards. These drivers aren't yet feature complete (eg. no video decoding, not very good power saving), and have limited support for their most recent hardware (HD7xxx). Performance-wise it's nothing to be extremely proud of (50% of catalyst for high end cards). But all in all, those drivers work. They don't spare any resources for upstream development (the team is about 5 people, so that is understandable)
- Intel - They write their own drivers, recently implemented OpenGL 3 into mesa (when their hardware started supporting it). Their drivers mostly have feature parity with their windows counterpart. Performance-wise, it's slightly worse than on windows, but nothing too dramatic.
ATM I mostly have ATI/AMD cards, and the OSS driver works well. Gaming isn't a priority though.
On the only intel card I have, I experience some weird issues (mostly related ro RandR), but it's a pretty old GMA4500, so you should be fine with their HD4000 series.
Personally I like ATI, but pragmatically Intel is a better choice if you want to go full OSS.
Which one have the best performances ?
ATI/AMD have the most potential for performance, Intel make the most of their hardware. For benchmarks see OpenBenchmarking