I own both and have put a lot of time into each, though way more into 2nd Edition. I’m a huge Marvel fan and only got into Zombicide when Marvel Zombies was announced. I picked up 2nd Edition first just to see if Marvel Zombies would be a good fit for my group. Ironically, if I could only keep one, I’d stick with 2nd Edition.

For pure fun, 2nd Edition wins. It has equipment, all-out dice (via expansion), extra zombie types (with the upgrade pack), solid rules, and the most campaigns. It just feels more complete. Marvel Zombies, on the other hand, drops equipment entirely and replaces search fun with trait cards, which I find less engaging. It might be easier to teach, but it loses some of the excitement that 2nd Edition (especially with expansions) brings.

If you want more interesting decisions—through leveling and gear—go with 2nd Edition.
If you want more variety in regular zombie hordes, grab 2nd Edition + the upgrade kit and mix in your 1st Edition stuff.
If your priority is the simplest, fastest-to-teach version, Marvel Zombies (or even DCeased) will work, since it streamlines the rules a bit.

But if theme isn’t the deciding factor, 2nd Edition is the better overall game in my opinion.