The differences are pretty drastic if you ask me,
Having gone to a state school I can say the classes are much much larger than private schools and you get virtually no personal attention, most of your discussion sections which are smaller will be taught/moderated by student teaching assistants...in state students get discounts but if you are out of state you generally pay alot more, personally I only think it is worth it if you are going to a school in your state and can take advantage of the price savings, if you are planning on another states school you would be better off putting the money to private....
with private you pay alot more but you get more personalized attention, better resedencies, better food, generally better campus....
I went to small private schools all my life and wanted to go somewhere big for college, from a social standpoint it was fantastic, from an education standpoint it could have been better, or rather I could have been better as I was used to personal attention and having others manage my time, with the state school they don't care about you as an individual so you have to watch out for yourself and make sure you do everything.
the good is that I have zero debt and it was far cheaper than others I know.
With BU specifically, while it is private it is also rather large....I have known many who do very well there and others who failed out...it is also in an ideal party location so it is easy to get sucked into the club crowd being right near lansdowne street....
good luck