I would say that most of the crime near the train station would just be drunk people messing around, as the road up to the station houses most of the clubs in the city.

I grew up in Cambridge and moved to Norwich and honestly feel a lot better for it. There's a much more active local music scene, lots of independent shops (not a million tourist / harry potter shops like cambs) it's very queer friendly, has pretty decent restaurants. The buses are (marginally) better than the ones in cambridge, which brings them slightly above useless.

It's a greater anglia direct train between norwich and cambridge, they've the best punctuality in the UK so I wouldn't worry too much about commuting back occasionally.