KGMU was established as early as 1905 while AIIMS Patna was established recently in 202. So the former seems to be more experienced with better opportunities and senior faculties. Let's look at these institutes one to one for a better understanding.
KGMC is one of the prominent colleges in north India and is preferred to many colleges in Delhi. The students here are called georgians
KGMC
AIIMS Patna
All in all, considering the AIIMS tag and the fast-paced growth the institute has witnessed, AIIMS Patna is the best choice for you.