Here is my honest observation of both these medical colleges.
My friend studies at Osmania Medical College. According to him, Osmania does not have good facilities. First of all, the college and hospital are located far away from each other. The hospital infrastructure is in a poor condition. The faculty does not teach well, they basically teach from guides. No proper teaching schedule is followed, and campus strikes are very common.
AIIMS Hyderabad is very newly built. But it has top class faculty. Unlike Osmania, the teacher-student ratio is good. Moreover, around 200 acres of area is allocated for sports activities.
So I would suggest you choose AIIMS Hyderabad over Osmania.