First you need to understand the basic difference of these colleges both are government funded hence charges less fee but the difference which matters is their autonomy generally autonomous colleges has freedom to design their own curriculum and conduct their own exams and open campus in various other places.they also adopts new concepts and techniques early than government college Once these colleges become an autonomous institution they become a deemed university ie. then they can offer various other courses and even PG courses. These colleges can get funding from the private sources too.

Its not necessary for medical students to opt between these too you should consider the ranking of the college and the most important thing it totally depends on you.