I'm not an expert on this but I'll throw in my 2 cents.
The GMO is a way for them to get extra time out of you. The GMO to me is the downside of the Navy HPSP. If not for the commonness of the GMO in the Navy I'd think that branch sounds the best of the three.
My impressions of the biggest negative differences in the branches
AF: The AF docs complain the loudest
Army: Good chance of spending a lot of time in the desert