There was a lot of public uproar in Texas several years ago when we began allowing them for game animals because some said it was cheating and people though deer were going to get killed with crossbows at 100+ yards during archery only season.
Fast forward several years and we have come to find that public hunters with crossbows are usually no more successful than conventional archers regardless of the bow being used and average range is around the same as well, regardless of the bow used.
The biggest complaint heard is animals jumping from string noise resulting in either a bad shot or clean miss. Apparently, like Frank pointed out already, they are quite noisy.