Manbearcat
Legend
I dig the playbook and company. The Fighter sounds like what we expect, and that's good. I like the ability names chosen. I think having a couple of base abilities right away is a good idea.
For the Avengers, the focus on cohorts and experts jumps out at me as a bit odd for the concept, but that may be in isolation without others to compare it to, as you guys suggest. Otherwise, it seems solid.
I would imagine that once you have a skeleton for each and maybe see them in play, then you can shift for thematic reasons as needed.
The focus on a Cohort as a member of the Watch and a Quartermaster Cohort is straight-forward.
Batman = Company
Commissioner Gordon = Cohort on the Watch
Alfred/Lucius Fox = Quartermaster