You should opt for AIIMS Rishikesh. It is more developed and offers better infrastructure. It runs super specialty courses. AIIMS Rishikesh also has a better faculty base compared to AIIMS Patna. It has a fully functional hospital with 24*7 emergency, more than 26 operation theaters, CCU, ICU, and NICU. Also, it has 3000+ opd.
Among all peripheral AIIMS, AIIMS Rishikesh has the highest number of PG seats.
AIIMS Patna is better considering many factors that include patient load, progress, learning environment, fast-developing hospitals, expanding wards, modular operation theatres, hostel accommodation, etc.
Other than patient load and infrastructure the other important point that you should consider while choosing the institute is academics. Which is great at AIIMS Patna and can be clearly observed in the PG exams. More than 40% of students secure a place on the first list for counseling.
There is a proper curriculum schedule designed for lectures, ward postings, and regular class tests. The institute also imposes special emphasis on co-curricular activities like the Annual Cultural Festival- KAIZEN, AVISHKAR CLUB, and many more that help in your overall development apart from studies.
Now coming to the comparison, it is quite difficult as both the AIIMS have their own advantages and disadvantages. So it is your personal choice which one you should choose. Consider different factors such as the weather, proximity to your home, patient load, scenic beauty, etc.