There is no 'badge league', but you can still compare badges on an individual (badge or user) basis.
For starters, you can see how many of a particular badge has been awarded by clicking on the 'Badges' Tab.
Clicking into a Badge from this page will then show you the breakdown of who has earned the badge (and when they earned it). For example, here's Altruist:
If you visit a user's profile, you can also see the breakdown of which badges they have earned. Clicking on a Badge on a User Profile will then show the breakdown of the questions/answers of where it has been awarded (if relevant).
For example, here is mine:
Those are the best ways to compare badges as they exist currently.
Note: While I'm sure you don't do this (and wouldn't dream of it), I think it's worth mentioning for future readers:
Earning rep/badges is fun, that's why they exist! But the best way to get both is to contribute to the site in a genuine fashion: Don't be the person begging for upvotes or spamming links to your posts (on or off-site) to generate views.
If you focus on the genuine quality of your contributions you'll find the badges and rep will flow naturally.