I was wondering, what is it exactly that moderators do besides closing and removing questions. I know they moderate comments and such if they break the rules, but what else? And >10k users are supposed to be nearly as "powerful" as moderators, what's the difference there?
The abilities available to 10K users are documented fairly well on MSO here. The major difference between 10K users and Moderators are that moderators have binding votes, therefore there is no 5 user vote rule in place. Furthermore the function moderators can perform is describe on the blog here.
Moderators can also suspend users, do mass retags, and view and deal with spam users and posts including locking posts, merging posts, converting posts to CW and deleting posts instantly. The same with users where we can merge or destroy user accounts. Lastly there is small abilities like removing bounties to migrate questions and recalculate user reputation scores. We can also delete and edit comments. Oh, and lastly we can set system messages.
There is also some other lightning bolts available to moderators which aren't publicly mentioned since... Well where would the fun in that be?