Not sure where monk stands with it's stats on full allagan. But as far as bard goes the game forces mixing and matching to even get close to the acc cap, with full allagan we are about 50 acc off from the cap.

Unless one set of gear is higher ilvl than the other it's honestly better that it does force you to mix and match as it actually makes you think on gear choices. Yes the sets may not match(until 2.2....) but for now it's either look at the stats they give or gimp yourself and your raid by not having the required stats to hit things.