This answer may vary from person to person but Maulana Azad Medical College (MAMC) is a well reputed and much older institution. Hence it has years of educational experience. On the other hand the AIIMS are relatively new and require a lot to learn and develop to be considered at par with MAMC.

MAMC:

• You can totally rely on the things taught here. As all the classes are taken by some of the experienced teachers.
• Their years of experience provide proper guidance on how to approach any situation.
• They have a gigantic campus, attached to notable hospitals like - Lok Nayak, GB Pant and Guru Nanak Eye Centre.
• There is a 50% DU quota for PG admissions.
• They have a batch size of 250 students, which at times could feel crowded.
• Being in Delhi, it has access to many good coaching institutes.
• Getting proper accommodation may take time.

Other AIIMS (except New Delhi):

• Campus is almost new and has well equipped labs and equipment.
• Almost everyone gets a hostel from day one and hostels are really in good condition.
• Batch size is small.
• Faculties are a mixture of new and experienced professors.
• AIIMS Patna does not offer any PG courses.
• Except AIIMS Bhubaneswar and Bhopal, other AIIMS do not offer PG degree in all courses.
• AIIMS Guntur and Nagpur function from their temporary campus. 
• Many departments in other AIIMS are not fully functional.
• There is less accessibility to good coaching institutes for PG preparation.
• There is no 50% institutional quota.

Therefore, MAMC, overall, is much better and reliable as an institution. MAMC promises certainty. So it will be better if you go for MAMC. AIIMS Bhopal, Bhubaneswar , Jodhpur and Rishikesh are developing fast, but AIIMS Patna, Raipur, Nagpur and Guntur are still lagging behind.