One that I've encountered is that I had trouble setting up live streaming to youtube with libav. Something weird with the rtmp code, with ffmpeg it worked out of the box. Not sure if it matters that it was on a raspberry pi.
This was my experience in using ffmpeg with an unrelated rtmp pipe as well. libav caused a ton of very strange and non-reproducible errors that were inconsistent. The switch back to ffmpeg cleaned up 90%+ of the problems.
