When you enter/exit towns, it's a black screen for, if I recall correctly, about 10 seconds. Entering/exiting buildings or changing screens in a dungeon has a similar wait time, though it might not be as severe. I'd need to load it back up and check. Opening the menu screen took a while, too. That was probably the worst offender, ugh.
There was also a little hangup before and after battles. If you've played the Super Nintendo version ever, that might drive you bonkers, but if not, maybe that can be a case of ignorance being bliss?
Super Nintendo and the DS are the definitive ways to play Chrono Trigger. I wouldn't call the persistent lag in the PSOne Classic version game BREAKing necessarily, but it hurts (more if you've played the original or DS version). It slows the game down, and when that happens, it can diminish one's drive to finish it.