i don't think that turning in the deposit the day of the deadline will matter, the housing people don't get your form until about a week from now anyway, and once they do the assignments are based on a computer-run lottery system for fairness, not any pre-determined order. While a bad lottery number could always change things, you could easily get either.
My guess would be that the triples in traditional dorms would run out faster, I think there are enough modern doubles for almost all of the people who request them. I've heard that the traditional dorms (more the doubles than the triples, but still...) are a bit more popular with freshmen though, the traditional dorms are usually a bit more social, partially due to the hallway layout. So you'll probably be alright in either case
