Do you have examples? I currently have libav on my Debian machines and ffmpeg on my Ubuntu machines, but haven't really noticed a difference for my needs. I'm not doing anything too complex, admittedly.
Example: ffmpeg -i doom4_trailer.mkv -acodec copy -vcodec copy doom4_trailer.mp4
Pretty simple, right?
libav:
>[mp4 @ 0xa33800] Application provided invalid, non monotonically increasing dts to muxer in stream 0: -83 >= -83
>av_interleaved_write_frame(): Invalid argument
(premature exit)