Although it's never really discussed in the movies, there's really one big event to convince him to destroy the DeLorean.
Namely, a bumbling aged idiot named Biff was able to figure out how to steal it and work it inside a day, destroying everything Doc had in the process. It's easy to use nature was it's danger - power like that never should have slipped out of Doc's hands.
I agree with comments and the answer from Charles that a quieter life and family gave him the distance and time to rethink it. He had really invented a wondrous thing - properly controlled, and kept safe in the right hands, it could be done right. My own thinking is that this led to his new design. It's a lot harder to steal a train, he had experience with that. We never see the inside of the thing, but I imagine a steampunkish design with physical locks that only he would know how to operate. It would be a far cry from a hop in and go vehicle that a car represents.