It is difficult to compare AIIMS Bhopal and MAMC. The former is run by AIIMS, directly under MoH&FW. While the other is run under MCI. There is no doubt that MAMC is one of the finest medical institutes in the country. But it is quite old. If we compare the growth of the institutes then it is safe to say that AIIMS Bhopal has progressed much faster. 

NEET toppers choose MAMC. On the other hand, the AIIMS tag is also greatly valued in the medical circle. AIIMS follows a different pattern of education. While being one of the oldest medical institutes, MAMC offers a better experience level in every aspect of medical science. In near future, AIIMS will stand way ahead of the old institutes. 

Both of these are great options. Which will be better for you depends on the parameters you are using to judge these institutes.