I would go with linux since I already Im a linux user and love archlinux, but groovymame never worked. Crashed before doing anything.
Win 7 and Vista complicate the matter of custom modelines, so only XP, 2000* and 2003* are suitable for GroovyMAME with CRT EMU driver.
On tests I did on my emulation system (Athlon 64 3000+ Single Core, 1.5GB DDR1), with GroovyMAME compiled by me with all the optimisations possible (bits, proccessor family etc), XP 32bit performed better.
Offcourse AMD cpus and MAME don't really go along well, and my system overall doesnt justify using 64bit.
So In my opinion, for old proccesors like Pentium 4 and AMD K8, go with XP 32 bit. For anything more recent go with XP 64bit.
*Didnt test, should work though