There are two families of drivers: open source and proprietary.
AMD has open sourced it's headers to the linux community, and is actually paying some pretty good devs just to develop open source drivers, just like Intel does. That means that the open source drivers for AMD and Intel are getting better all the time, and for AMD that means that you can actually use the open source driver for daily computing, and it's completely stable and safe to use. The proprietary driver still performs a bit better and has a few more features, and you can use amdcccle like in Windows to configure the card, but as with Windows drivers, it's sometimes not completely stable, but also, if you're coming from Windows, you're not even going to notice any instability, because linux won't crash or bluescreen or anything, at worst you'll take a graphics performance hit that you'll hardly notice unless you've been using linux for a long time, or some minor artefacts, not massive texture fail or any of the stuff you get when Windows tries to not crash with unstable drivers.
CrossFire has been fully supported in linux since 2008, and depending on what application you use it for, scales better than in Windows.
OpenGL works, Shaders work, OpenCL works, DPM works (with the 3.11 kernel also with the open source driver), everything just works nice and stable.
Also, the card will not overheat in linux, at all, because DPM is fully supported now, so you can overclock without fear of breaking anything, because the reliability is much higher than in Windows. In Windows, you overclock the GPU with software, then there is one of those frequent system freezes in Windows, and your card overheats and is damaged, not going to happen in linux.
What might happen, is that the average temp on the card might be a little higher than in Windows, because linux uses hardware in a completely different manner. Linux actually USES hardware, it doesn't need certain GPU specs or CPU specs or whatever to be able to do a particular thing, but it will make maximum use of all the hardware available to give the best performance possible. That's why CPUs tend to get a little hotter in linux than in windows sometimes, because linux actually uses all the cores, and gets the best performance and efficiency, but at the same time, the safeties against overheating are much more reliable in linux than in windows. So for instance, if you use a photo editing program in Windows, you might see a hell of a CPU load and a very cool GPU, whereas the same program in linux, will only use a bit of CPU, but will do a lot of OpenCL calculations on the GPU, running the GPU a bit hotter, but also getting better performance and more efficiency.
Multi-monitor is self-evident in linux, and every monitor can be configured separately to the extreme. All modern DE's natively support workspace management on multiple display interfaces to a degree Windows can only dream off.
AMD also has pulled the XMir patches from Canonical, unlike Intel. Not that many people care that much, but basically, that means that even Ubuntu with Unity will run on AMD GPUs, unlike on Intel iGPUs (Intel does this because they have other plans for linux, they actually don't want Ubuntu to gain momentum in post-PC desktop linux, because they're working themselves with Samsung and the linux foundation on their own - also AL2.0 licensed, just like Mir - commercial linux platform.
AMD is a very good choice for linux, because most if not all modern AMD platforms support AMD-Vi, since the 790FX chip all AMD chipset based mobos have full linux crossfire support, AMD CPUs have more cores for less money, and multiple cores just scale better in linux than in windows, and AMD GPUs work incredibly well with OpenCL, which makes an all AMD system a very good performer in linux (it's like having a CPU and an extra FPU to go with it), even with open source drivers, which is still a safety bonus over proprietary drivers, and using open source drivers means not tainting the kernel, so you can still get support for your install in case of problems, which is impossible with a proprietary driver headers tainted kernel.