There are those that prefer long periods in one location to really get into the culture/city.

Others prefer the see-as-much as possible in whatever time frame you have available.

I fall into the latter category. I'd say make a list....see as much as possible in Switzerland and then move on to Italy. In Italy, I think you can hit the main sites in Rome in 3 days....maybe 2 if the Vatican, Coliseum, and Forum are your only "can't miss spots". Venice and Florence can be 1 day trips if pressed for time.