I love all animals so I couldn't choose one over the other.
Rabbits: they're personalities are all different and it depends on how you treat them!
1)Usually bunnies are funny little guys who jump around and will put a smile on your face with all the silly things they do.
2)Yes it is best to bring your bunny to the vet, and it's best if you spay/ neuter them. It lowers aggression and risk of health problems
3) minimum cage size for two would depend on what kinda cage your thinking. I'll give you some ideas.
4) I'd suggest giving a whole room to a bunny. Whether that's a separate room or your room where they can run around and play. They need lots if exercise! Also best diet for rabbits would be very little pellet food and should consist of a lot of veggies and some fruits! Also ease check your near by shelter do not buy :)
Rats 1) their personalities change as well, all the rats that I've owned have been pretty chill funny little guys.
2) rats have to go in a pair+ it doesn't matter! UNLESS, the rat is aggressive and needs to be housed alone.
3) minim cage for 3 rats, I'd say the best cage would be the critter nation, but the one that's two levels. I forget what model that is.
4) once again please check your near by shelter! Also, most commercial rat food is not good for them, I'd suggest making your own food! Also they as well need to be out if their cage everyday!
Bunny cage:
http://youtu.be/NUc-tAdiPYM
Ideal rat cage: even though hers is very crowded you don't need that much.
http://youtu.be/ZZyQQp2AOEM