Is it better to apply to a less prestigeous PhD Program, or do research for a year and reapply?
Doing research for a year and reapplying would definitely be the better option IMO. Even though it's true that when it comes to performing research, it matters less where you do it, there are certainly undeniable positive effects from getting a degree in a prestigious university - from the peer group you'd be surrounded with to the visibility your work could get later on. After all, the research that you will do during the one year is not going to get wasted. Even if it doesn't get published, it only sharpens your ability to perform research.