You generally shouldn't ever install the old DivX 3 codec, as it is known to cause all sorts of problems. FFDSHOW can decode anything old you have lying around that was encoded with the old DivX 3 codec.
To be clear, libavcodec (the core codec of FFDSHOW) is a general purpose MPEG-4 decoder. It handles (among others):
DivX (all versions)
XviD (all versions)
3ivx (all versions)
Nero Digital ASP (old version)
Nero Digital AVC (new version)
Apple's MPEG-4 ASP (old version)
Apple's h264 (which is MPEG-4 AVC in a MOV wrapper)
x264
WMV (most versions)
theora
snow
VP6 (the flash codec used by YouTube)
and many, many more...
For any of these codecs, you don't need to install the individual codecs themselves if you have FFDSHOW. You only want/need the "real" codecs if you want to use those codecs to CREATE videos (and then you generally only want the newest versions installed). Obviously, if you uninstall FFDSHOW it will break playback of the video on your files because it is handling the playback!
Many "old" versions of codecs are well known to cause playback problems, especially the old hacked DivX codecs. You really don't ever want these installed. It annoys me to no end that people continue to include these in many of the stupid "codec packs" out there. If you have FFDSHOW, it should handle the decoding of the vast majority of the formats you encounter.