I guess each has it's own advantages and disadvantages. Quick games forces you to try and spot the best move quickly and this may help in long games so that you wont accidently overlook a better move. In terms of long games helping quick ones, I personally don't see a connection. Long games need quite a bit of thinking and analysis during the midgame and endgames, something you can't tend to do in quick games.
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At the end of the day it is better to be a strong player in longer time controls. Beating good players in long games shows that you have an understanding of the game.
Anyone can win in quick games, even by playing terrible, so i guess the question to be answered is:
Do you want to play chess simply to win or do you want to develop a great understanding for the game?! Personally, i dont care if i win or lose but i always ask myself did i really understand the game. When i understand the game, i am happy even if i lose. If i lose the thread of a game i feel disappointed by making sure i analyse later on to learn. Inotherwords, i rate understanding more than winning.
Ok, so you might want me to reply to the real question you asked now. Well, i must admit that since i started playing quick games online, it has helped me with my longer OTB games. Firstly, it has improved my tactics and made me a much sharper player. (really, i cant say by how much!)
Secondly, because you can play a much greater number of quick games in a given time, your familiarity with opening positions will also improve. My opening play improved alot even playing 1 min games but you must remember that this all takes time. You wont see the results overnight and always try to balance the time controls you play. You shouldnt neglect playing long games (or quick games) because they really do compliment each other in the long run i think.
Ive always wondered, does playing quick games help you (in any way) in long games? And vice versa? Ive been in 1700's here on chess.com in long, never have i been in 1700's in quick, now im doing bad in long but good in quick, its just very weird ...??? The only way i can see quick helping long is in a time situation - and long helping quick by strong moves.