CoreAVC is widely regarded as the fastest MPEG-4 AVC (aka h264) decoder out there, and the one that results in the lowest CPU usage during decoding. The most common use for it is for slower machines that couldn't otherwise handle the decode of a particular type of video stream (1080p h264 video on a Pentium 4, for example). It is perhaps the best MPEG-4 decoder out there, but isn't free, so isn't nearly as widely used as FFDSHOW.
Aside from assorted bugs (which both FFDSHOW and CoreAVC suffer from in roughly equal quantities), there is no quality difference between the two major decoder options.
Being an open-source community developed project, FFDSHOW tends to evolve more quickly (have more versions, more often -- at least since the Tryouts project got going) which leads to certain bugs getting quashed faster. However, this can also lead to new bugs cropping up more often, so it's pretty much a wash. CoreAVC revs more slowly and is tested more thoroughly before release, but is tested on a much more limited install base.
It's pretty much a wash. If you're supporting an older machine, and you're willing to pay the licensing fee, CoreAVC is a very good choice. FFDSHOW is good enough for most people, though it is advisable not to live on the bleeding edge of FFDSHOW development.