Gamecenter has extremely poor adoption so I would not recommend you lean on it.

Gamification services in general can be pretty hit or miss. Here are a few for your to explore.
https://badgeville.com/
https://playlyfe.com/
https://www.playbasis.com/

I'd note that these type of leaderboards can often do great things to a product that is already working, but if you are creating something that doesn't already have a bunch of users who really like what you are making... it's a tough road ahead if you outsource (you need to in house the effort).