Why Perugia is more rich then Terni?

For several different reasons.

Perugia is a tourist city while Terni has almost nothing to offer to tourists, excluded a few spots in its province. Perugia is the capital of the region and then it has been provided with more infrastructures and connections than Terni and this fact has contributed to elevate the pro-capita incomes of Perugia's inhabitans. Perugia has a very important University, attended by thousands of Italian and foreigner students and also this contributes to rise the general richness.

Perugia has many diversified industries that have grown up in the years while Terni has always had a kind of mono-industry (steelworks) that, while in the past has guaranteed a good level of wages, in the last times (mainly after they've been sold to a German company) this sector is year by year sadly declining.

I'm not living in that region and it's also possible I've forgot something but the ones here above should be the main reasons of the different richness.