In my past experiences with both players, Windows Media Player uses a bit more RAM than VLC when it comes to music, though its the other way around with videos.
Currently, when playing a song in each (tested with mp3), WMP uses around 20 MB RAM and 5-7 CPU power. VLC is using 1-2 CPU and less than 10 MB RAM.
However, when it comes to videos (tested with avi and mp4), WMP uses about 30 MB RAM and 10 CPU on my PC. VLC uses over 45 MB RAM and 10 CPU.
System resource values above are estimated averages based on experiences with WMP 12 and VLC 1.1.
In terms of hard drive space, the WMP folder is only 6.28 MB but it does rely on many components of Windows which are located elsewhere on the system. VLC's installation folder is around 77 MB.
Both work quite well although there are always a few formats that WMP just can't handle. If you don't need the libraries features of WMP, then I would highly recommend VLC because its lightweight and supports many more formats than WMP and iTunes does.