Try running Xonotic/misc/tools/the-big-benchmark/the-big-benchmark.bat and see what happens. It will run through all 7 different quality presets and benchmark. If at some point there is a problem with a certain quality setting then you would always see a crash when it gets to that setting. Here are some instructions for the benchmark:
http://forums.xonotic.org/showthread.php?tid=2562
If you could then post the output log file from that if there is any crash it may help diagnose any problem. As of right now no-one has reported back running Xonotic on a Radeon HD6800 so it may be you are the first to find an issue.
As you are running Radeon (and I'm afraid right now Crossfire won't do anything for you as the Radeon driver does not have a profile set up for Xonotic) you can expect more problems that on an NVIDIA card. It is an unfortunate thing that AMD's driver is more prone to issues than NVIDIA's for OpenGL. It may however be a simple thing like disabling OpenGL 2.0 shaders in the game. Please report back if you find anything as it may help someone else with similar hardware.
http://forums.xonotic.org/showthread.php?tid=2562
If you could then post the output log file from that if there is any crash it may help diagnose any problem. As of right now no-one has reported back running Xonotic on a Radeon HD6800 so it may be you are the first to find an issue.
As you are running Radeon (and I'm afraid right now Crossfire won't do anything for you as the Radeon driver does not have a profile set up for Xonotic) you can expect more problems that on an NVIDIA card. It is an unfortunate thing that AMD's driver is more prone to issues than NVIDIA's for OpenGL. It may however be a simple thing like disabling OpenGL 2.0 shaders in the game. Please report back if you find anything as it may help someone else with similar hardware.
I'm at least a reasonably tolerable person to be around - Narcopic