Personally, I'm a big fan of Chicago style pizza. I haven't heard of Neoapolitan but assume it probably has some elements borrowed from the Chicago style.
"probably has some elements borrowed from the Chicago style."
LOL - the exact opposite, actually.
Neopolitan is thin instead of deep-dish. The idea is to blast it at like 900 degrees, but only for 1-2 minutes, so they keep it thin so it can actually cook in that time.
That said, Chicago style 'deep dish' is a personal favorite too. In fact, it's been a while since I made some - maybe I should go find my spring-form pan again :)
I don't get the hate Chicago-style pizza gets. It's a different thing than neopolitan-style and New York-style. That's ok, they're just different, and I like all of them.