The proprietary nVidia drivers won't compile on kernels 3.10 and up, but there are patches available. However, those patches break other proprietary kernel modules that use dkms/akmod, like Virtualbox for instance.
So as long as you have an old distro, with no later kernel than 3.9, you can use the nVidia proprietary drivers (3.8 is a LTS kernel, I would recommend that one, and I would recommend Manjaro because of the on-the-fly or in-session kernel changing function with mhwd).
In general though, if you offset performance of nVidia and AMD cards on an older kernel, they're very comparable, but if you offset nVidia performance to AMD performance on kernel 3.11, AMD really takes off in performance, it's the best performance of any card in linux until now.
Now I always get in trouble when I start to write technical linux stuff, but yolo right:
1. AMD graphics cards have an OpenCL performance of 2.5 to 5 times the performance of any other graphics card. If you use applications that accelerate the system with OpenCL (and there are a lot of those, even simple things like LibreOffice), or if you revel in pyrit or hashcat sessions, AMD is the only way to go, a 270/7850-like card will cost about 150 USD with 2GB of VRAM, and is a very powerful GP-GPU in linux;
2. Now I get technical: AMD has a lot of running open source projects that tie in with their long term policy of what they used to call the "Fusion" project, which they now call the AMD Hybrid Architecture. AMD has been working very hard on this, and they have developed a set of tools that have lead to other tools, including what they call "Mantle". The base toolkit that generates all these possibilities for advanced GP-GPU use of AMD graphics cards, is called "AMD APP", and is licensed under the AL2.0 license, and can be downloaded for free here: http://developer.amd.com/tools-and-sdks/heterogeneous-computing/amd-accelerated-parallel-processing-app-sdk/.
With this toolkit, you can implement your own GP-GPU system acceleration. This is now being used by a lot of devs for game engine acceleration, and goes much further than Mantle, which is like a castrated version of AMD APP for the windows and PS4/XBone consoles. It works on any card with the CGN architecture, which means anything from the HD7000-series on. So 200 USD basically buys you a couple of teraflops of GP-GPU performance to add to the performance of your CPU.
The entire benefit of AMD APP is only available in linux, and preliminary tests have shown that an average system performance increase of about 40% in the very early experimental stages is quite common. That is CPU performance, just because of the fact that the CPU can offload all the FP-operations to the much faster many-core GP-GPU. Basically, the only thing AMD APP does is provide a translation layer for the CPU instructions in software packages to instruction sets that make the CPU use the GPU as FPU. In the next phase, as devs will use AMD APP more, there will be no difference anymore between CPU instructions and GPU instructions, they will sort of speak the same language, and will know how to divide tasks for maximum efficiency and performance. Pretty much the same thing that Intel is doing with the Xeon Phi's, but they can't seem to get it sorted. AMD is much more advanced in this respect, and has been deliberately slacking on driver optimizations for games to be able to implement their "Fusion" concept. In the future, this will mean that you can actually scale GP-GPUs, and get a much higher performance for less money than by doing a CPU upgrade. Mind you, only in linux. AMD is selling mini-ITX HPC's now based on APU's, with slots for adding GP-GPUs, and thsoe little boxes are already being used for prototyping, rendering, fluid dynamics simulation, big data analysis, etc..., and they work, they are proven to work very well. I have been busy testing this thing myself for a couple of months now, and the compute performance is just stunning for the price of these systems. That is the future AMD sees for itself. They don't have an ARM project, but they sell the stuff that ARM software devs use for efficient development, because an emulated ARM on QEMU in linux works more efficient than developing on an actual ARM platform, and new ARM chips come out almost every week, so devs just can't keep up, unless they use a powerful emulation platform. I know most users on this forum don't want to hear about it, but the AMD fusion platform, as a combination of CPUs and GP-GPUs, will be the first next-gen PC platform (and Intel wants it too, they're working like crazy on it, so it's going to happen any way you look at it), which will be linux based only.
3. nVidia does not have an answer to the APP technology by AMD, and they have no intent of offering GPU cards with an x86-compatible instruction set. They want to keep their GK110 and GK118 platforms proprietary and seek not integration and no open source support. The compute performance of nVidia cards is also pretty dismal in comparison to AMD and Intel "plug-in compute" solutions, with AMD GP-GPUs and Intel Xeon Phi performing similarly, but AMD solutions being 4-5 times cheaper, and multi-functional, because their cards are still damn good GPU cards also, and the Xeon Phi is compute-only. Frustrated by the lack of action on behalf of nVidia, there are two projects that aim at delivering an open source GP-GPU functionality for nVidia cards. There is a third one based on CUDA libs, but that is not open source, so the project has been pretty much abandoned. The two projects that are still in development are the system that RedHat is making with cooperation of nVidia for expanding linux CPU-instruction handlers to nVidia GPUs, which requires IOMMU, because a translation layer is added in software to make the GPU and CPU work together. There is not much known about this project, and it's pretty hush hush because RedHat has received proprietary information from nVidia to be able to realize this project, and nVidia had promised to open source the necessary information, but the webpage where this information would be posted, has been dead in the water for weeks now since they made that promise, so that doesn't look good. Another project that is still theoretically alive is kgpu, which is a GP-GPU project for nVidia cards that is hosted in the google code project, but there is only one developer, and he's paused the project because he's working on another project called snap.
Conclusion: whereas last year, noone would have expected that, it now seems that AMD is a much better choice for linux users than nVidia. AMD is metaphorically working on the alchemy of making gold for linux users, and it's not just theory, it's really happening and the results are there to prove it, and a lot of software devs, whether linux/crossplatform game engine using game devs (Unity comes to mind, which is also the first engine to have CastAR support, and that is a big deal for the future of next gen PC form factors and interface design), or production software devs, are jumping on this AMD technology, and when that software comes out as soon as mainline linux has migrated to the Wayland X server, it will mean a true revolution in PC performance, and nVidia will fall back to ARM development and legacy windows graphics.
That's all from the point of view of linux of course, there will be no performance revolution on closed source operating systems. In fact, this is also proven by the fact that the new Intel Atom-platform machines that are coming out, have an up until now unbreakable Windows 8.1 hardware bootlocker. Even after flashing the UEFI and removing chips of the mobo, linux hackers have not yet succeeded in making these new machines load anything else than Windows 8.1. And with the good performance of those Atoms, and the price which is close to Core i3 systems for a much lower production cost, it's clear that Intel sees the Atom platform as the new Windows-PC platform, which will be completely locked down, before moving on to more advanced architectures for linux only that will harness the power of CPU and FPU/GP-GPU units.