I grew up with both shows. Loved them both, but here's the difference: Full House was good, whereas The Wonder Years was not only great, but perhaps the greatest show in the history of television. That's the difference, and that's why this is a no-brainer for me. The Wonder Years gets my vote and it's not even close.
Full House had its moments, but it was still highly cliche, and it took a lot of short cuts to solve every problem each character had within a 30 minute duration. The Wonder Years was just the opposite. It was innovative, and gave us compelling drama each and every episode, while still getting an uncountable amount of laughs out of you at the same time.
This is really not even a competition. Why is The Wonder Years up by only one vote? Come on, people.