RYV Parker is a responsible adult and a good father/husband. 616 Pete is a man-child. Just like how Spider-Gwen is a web slinging hero, while 616 Gwen fucked Norman Osborn pumped out 2 kids and got thrown off a bridge.
Their histories make them different characters.
Also the prerequisite for being batman is a lot steeper than being spider-man. With spidey you just have to be bit by a spider and have a desire to help people. With batman you need, a shit load of money, years of training in martial arts, an extensive background in psychology, the arts, computing, etc. etc.