AMD has yet to release any Catalyst driver that is compatible with X.Org Server 1.10 driver, but they are working on it. NVIDIA has had out beta drivers -- like is usual for supporting new kernel and xorg-server releases -- but their existing beta had been built against ABI version 9, which was the application binary interface up to X.Org Server 1.10 RC2. NVIDIA's engineers have now rebuilt the driver against version 10, which makes it compatible with the official X.Org Server 1.10 release. This new beta driver is tagged NVIDIA 270.30.
Download links for x86 and x86_64 Linux distributions are here. Beyond supporting the final X.Org Server 1.10 release, there is no other official changes mentioned. The NVIDIA 270.xx series already adds in some new features like an NVML shared library, more VDPAU fixes, 3D Vision work, and various bug-fixes.