From what I've seen, read, and heard...Ha
X-Men:
LE has the spinning Magneto disc, Iceman ramp (which some love, some hate - I think it's awesome), and the Nightcrawler pop ups. The BIGGEST game changer of those three would be the Nightcrawler pop ups. Spinning disc is cool (my wife loved that feature), and the Iceman ramp is a real crowd pleaser (everyone LOOOVED when it rotated). I saw Nightcrawler only a handful of times when I had the LE.
Avengers:
I don't know the differences between versions, I apologize. However I do know that the LE seems to have some weird hangup issues by Hulk that are sort of hard to fix. LE owners can probably help you out. I think the Pro is probably a great buy on this title since it can be found for a great price. But having said that, the LE is going for a really reasonable price, too. Pinside is full of VERY polarized posters - owners of Avengers love it, and those who don't hate it. X-Men had a bad reputation but has regained some popularity - Avengers really hasn't...
I think you'd want to play Avengers before you make a decision on it vs X-Men. If you enjoy a deeper game, I would argue for X-Men in this case. X-Men LE can be found for ~$5-5.5k, whereas Avengers LE is probably in the $4-4.5k range. If you're feeling really ambitious, you can try and hunt down a Pro of each and spend ~$6.2-6.8 and get them both.
Hope this has been SOMEWHAT helpful. I also hope someone who has played a lot of Avengers can weigh in to give you their opinions, too.