In order to determine, which of the two; AIIMS Nagpur and GMC is better, I have listed the pros of the two institutes individually. Go for the institute that appeals to you the most.
Pros of GMC Nagpur
It certainly is a decent choice for pursuing Mbbs,MS,MD etc .
Pros of AIIMS Nagpur
The AIIMS tag in itself carries huge weightage.
I would always suggest you go for GMC Nagpur as it has better facilities than AIIMS Nagpur and seems more promising.
No, GMC Nagpur offers admission to its UG, PG and Super Specialty courses only on the basis of NEET score. However, it grants admission on the basis of merit in the last qualifying examination for a few courses such as BPMT.