A big reason - aside from the quality testing - that Xvid gets recommended is that it lays out options for MPEG-4 ASP which DivX restricts (either as a matter of discourse or because it only allows them in Pro versions). So in short, Xvid is simply more customizable.
x264 is an H.264 implementation - it is not related to DivX or Xvid at all, aside from H.264 also being part of MPEG-4. In it's case, MPEG-4 Part 10, Advanced Video Coding (AVC) - DivX and Xvid are MPEG-4 Part 2, Advanced Simple Profile (ASP) encoders.
MP4 is a container, and it can hold ASP streams just as easily as it can H.264 - in reality, MP4 was the container they should have been stored in from the start, but there was too much scene reliance on AVI. While there are comparatively few AMVs or fansubs released in MP4 that use ASP streams instead of H.264, there are some nonetheless.
MeGUI (after installing, let it run update - it might be useful in the options to switch the update servers from 'Stable' to 'Development' to keep up with the latest version):
http://x264.nl/
MeGUI requires .NET 2.0 (
link). It requires input in the form of AviSynth scripts, so AviSynth is obviously required as well.