Both are good. Go where you can live in base or move to a base. If those aren't options, pick the one with the shortest commute.
I got hired at both. I took the ASA job, but I live in Atlanta. I have a friend at Eagle who has been there about 6 months longer than I have been at ASA. His relative seniority appears to be higher, and it looks like Eagle is hiring more than ASA is, so movement could be better there, but either one is good.
Good luck! No commute is priceless!