There are two AMD OSS drivers: the R600 and the RadeonSi. The R600 delivers more than 80% of the performance of Catalyst, and are the best choice for cards up to RHD6k series. The RadeonSi is still in development, but is getting better literally every week, and only works well with kernels that have merged the functionality of the RHD7k and R series. If you use an old distro, that is not up-to-snuff with kernel development, you will never get good performance out of the RadeonSi, until that distro catches up, which can take a very long time. If you insist on using an older distro, like Ubuntu 13.10 for instance, you can still compile a newer kernel yourself from git, but expect extreme breakage with Unity and XMir. This problem does not exist with community Ubuntu distros, i.e. non-Unity Ubuntus.
There is however a solution for Unity Ubuntu users, there is a community repo somewhere that provides packages that allow for installation of the kernel 3.12.5 first build, which is not great but acceptable, and that prevents breakage. I don't remember the link, but I think it was an Australian project. I tried it when I tested Ubuntu 13.10, and it worked.
There will always be one point of low performance with the OSS drivers, and that's Adobe flash. This is not a driver problem, but a deliberate blockage by Adobe. The way Adobe does it, is quite crazy: when you're running proprietary AMD or nVidia drivers in linux, Adobe doesn't let flash use the GPU, so there is a lot of load on the CPU. This is known issue, and Adobe has made clear that they want it that way. On the other hand, when you use an OSS driver, Adobe prevents flash from even using the GPU, AND limits the CPU activity, so that you get the same flash performance out of an Atom N450 and an i7-4770. There is a fix for it, but it involves a little hack, and most users that use OSS drivers, will not use flash anyway, but HTML5 instead, and that works just the same with OSS drivers and proprietary drivers. So it's a non-issue really.
In games, the AMD OSS drivers perform quite well. There is still some work to be done on the RadeonSi driver, but most of the lack of performance has been solved with the linux kernel 3.12.5-6-7, and almost all of it is solved by kernel 3.13. I use kernel 3.13 on a fedora install for gaming with RadeonSi, and the performance of the GPU in comparison to kernel 3.12 first build has all but doubled.
It's one of the reasons I recommend bleeding edge distros, this year, HSA comes out in linux, and the full HSA implementation in fedora release will be for August/September, depending on how fast Intel can sort its problems (and they still have huge problems), because fedora will wait for Intel to at least have a functional version of Beignet, even if it's limited, and for Intel to at least patch the huge graphics performance regression on modern kernels, but chances are, that it's a design flaw in Haswell (as I posted before Haswell was released, I had a netburst-feeling for Haswell, I think that feeling was right), and that Intel will release Broadwell in summer to offer a solution that is a bit of a closer match for AMD's amazing APU line-up, even though I believe that Intel will need about two years and another CPU-generation to catch up to Kaveri and Kabini, because even if Broadwell matches Kaveri, which is not very likely because Intel lacks the graphics experience, AMD can downstream Kabini units to Kaveri, and offer hexa- or octocore APU's, because Kabini proves that they have them ready, and they're just moving forward with the parking brake on for the moment (AMD also sells Intel CPU's, they have no interest in deteriorating the relationship with Intel, which has been quite good since 2009). People that use bleeding edge distros, will gain at least 6 to 12 months of early adopter benefit, as bleeding edge distros have everything laid out, tested and stable by summer, whereas non bleeding edge distros will only be able to start testing and integrating HSA for the October to December 2014 development releases. Ubuntu 14.04 is an LTS release, but will have to pass on HSA completely, and that will knock Ubuntu back considerably. 14.10 is just a development release, which have been getting hugely unstable recently, to the point of being very hard to use, and even if it's stable, Canonical will not be able to provide HSA integration by October, so Ubuntu users will have to wait at least for the 15.04 development release to even start trying HSA, and it will be hugely unstable, so by the time Canonical gets some stability in the implementation of HSA, Fedora, Gentoo and Arch users, will be using HSA in a stable manner for a year already. That's 25-33% of the life cycle of the hardware that it's running on, that's a lot of missed opportunity and investment write-off.