Both these AIIMS were established in 2012, both are centrally funded, and there are very minor differences between the two. Both AIIMS Rishikesh and AIIMS Raipur will offer good research facilities to you.
Location is another important factor. AIIMS Rishikesh offers a scenic landscape, while AIIMS Raipur offers a rich city life. AIIMS Rishikesh has theory exams, while AIIMS Raipur has MCQ based exams.
Hospital wise, AIIMS Rishikesh has a slight advantage, but academics and infrastructure wise, both are equally good.
Thus, you can opt for AIIMS Raipur without any hesitation.
Both are AIIMS 2012 graduates and are roughly comparable. In terms of research, there are numerous opportunities at AIIMS Raipur. The academic section promotes research on a proactive basis. It has the same facilities and receives the same funding. Every batch has a few people studying for the USMLE.
AIIMS Raipur is only 10-15 minutes from the city center, and there is plenty of development all around it, including all the markets, shops, and restaurants you could want. It all depends on your preferences; if you want to be in and around a city, Raipur is the way to go.
Rishikesh is a good option if you want to study in a natural and beautiful setting.
At the end of the day, both are excellent institutes that would give you a slight advantage in terms of brand value.