DivX vs Xvid
DivX and Xvid are multimedia compression codecs based on the MPEG-4 ISO format (MPEG-4 Part 2, also known as MPEG-4 ASP). Xvid first came out as an open-source alternative to DivX, with the name "XviD."
DivX is proprietary. Xvid is free software licensed under GNU GPLv2.
As MPEG-4 ASP is covered by patents, the legal usage of Xvid may still be restricted by local laws 1.
Xvid can optionally encode video with advanced features that most DivX Certified set-top players do not support. Files encoded with global motion compensation, Qpel, MPEG quantization, multiple B-frames or files that exceed the VBV limitations may not play back properly on DivX Certified hardware devices.
For example, Xvid specifies three warp points for its implementation of global motion compensation as opposed to the single warp point implementation of DivX. Enabling some of the more advanced encoding features can compromise player compatibility. Some issues exist with the custom quantization matrices used in tools such as AutoGK that automate encoding with Xvid. This can (depending on the decoder chipset of the set-top player in question) produce videos that have unstable playback and artifacts. However, most recent model DivX compatible DVD players have improved support for custom quantization matrices.
If you enable all the advanced motion search estimation options, QPEL, GMC, and all, XviD will be way faster than DivX (see the comparisons above).
In short, XviD will be always faster.
Both codecs can decode the other's output since they both are implementations of MPEG-4 ASP.
In comparison ITU-T H.264 / MPEG-4 AVC (also known as MPEG-4 Part 10) uses an exactly specified iDCT approximation to avoid this problem.