The HD3850 is DX9 and DX10 compatible. Windows XP is DX9 only. Windows Vista is DX9 and DX10, so the HD3850 is compatible with either operating system. To my knowledge, there are no Vista/DX10 ONLY games. Most, if not all, newer games will run on either operating system.
As rolli59 stated, there isn't much to be worried about when buying a new monitor.