In terms of performance, almost nothing since forever. 64-bit WMP rely on 64-bit codecs which in theory can benefit with more complex software-mode (running on CPU), but most codecs are written with hardware-mode in mind (utilizing the far more appropriate GPU).
In terms of compatibility, practically none. It's possible an exotic format is made with binary only codecs that's only available in 32-bit or 64-bit, but such format would be very niche.
In terms of security, 64-bit media player with 64-bit codecs may benefit more from ASLR with their larger possible memory address (4096 times more, which could be the different between practical and theoretical attack). Such overflow attack was the key behind Stagefright in Android, and there was multitudes of vulnerabilities on WMP relying on buffer overlow.