Navy still has GMO tours. They're diminishing but still exist. So if you're going into a more competitive specialty there's a chance you could serve as a GMO for a few years to accumulate points towards your military residency application. That being said, there are plenty of specialties including psych, FM, OB/GYN, etc that generally funnel you straight through into a Navy residency. GMO could mean going to flight or dive school to earn qualifications and then go work with the fleet. There are also battalion surgeons that work with the USMC. Every doc I've talked to who did it says it was one of the best experiences of their lives and wouldn't trade it for anything. So if you don't mind taking a few years off to fly in jets or work with SEALs, Navy is a great choice.
Navy also has fantastic duty stations (San Diego, Yokosuka, Rota, Naples).
Full disclosure- I'm a second generation Navy Medical Corps officer, so I'm slightly biased.