1. Baseball. Although ND wasn't a traditional Big East power in baseball, it did have one of the better Big East programs last year. The ACC is one of three power conferences in baseball, with the Pac-12 and SEC being the others.
2. Men's soccer and men's lacrosse. I grouped these two together since the issues facing them are largely the same. ND was in a decent, not great, conference in the Big East in both sports, and now they're about to join a monster conference in each sport. I'm not saying for certain that either team will take a tumble, but for both, the competition meter got kicked upward by several notches.
OTOH, I don't think men's basketball will have the sort of growing pains that many are predicting. I don't see the new ACC being any stronger (if even as strong) than the old Big East was. The main difference will be at the bottom of the conference: in the old Big East, you could pick most of the bottom six or so teams every year before the season began. In the ACC, the teams comprising the bottom of the conference figure to rotate somewhat from year to year. But that doesn't mean the bottom of the ACC will be any tougher, in any given season, than the bottom of the old Big East was. I look for pretty much more of the same: consistent 20+ win seasons, a few nice regular-season upsets, and an early exit from the NCAA tourney in most seasons.