If I had to pick one area to excel, and had everything else average, I would pick USMLE scores. They seemed to open a lot of doors for me. That being said, I'd rather have everything average, then have great board scores and lousy letters.
There are several reasons.
1) Lots of programs use board scores to screen. Good ones will get you past every screen.
2) The only objective comparison between applicants is their USMLE scores.
3) Do you really have to wonder if someone with 250+ A) Knows how to study, B) Knows how to test, C) is intelligent enough to learn the material inherent in specialty training? None of the slackers in my class had board scores that high. (Note, I'm not saying board scores are important in becoming a good doctor etc, just that really good ones eliminate a few worries about a residency candidate. You still don't know if the guy is a complete social loser, a sociopath, a lazy bum, a drug addict, an arrogant snob, a nerd etc.)