Having knowing people in both MS Ramaiah and Kempegowda Institute of Medical Sciences (KIMS), I can say that they are of the same standards when it comes to undergraduate teaching.
Even though it is said that doing MD in a private medical institute is not great, MS Ramaiah is better than all the above-mentioned institutes. It has been ranked 12th in the best medical colleges in India by NIRF and is very competitive to get into.
JJMC and BR Ambedkar are almost of the same level and come after MS Ramaiah and KIMS. So the overall preference should be MS Ramaiah, KIMS, BR Ambedkar, JJMC.