You're getting very different opinions, so you also need to know your own strengths and interests.
We flew into MXP from the West Coast US last May and arrived around 1pm. We were at our hotel near Termini station by about 3 or 3:30, but everything went super smoothly with luggage/passport control/train catching. We walked to the city center and visited the Duomo and the rooftop (we didn't have as much time as we would have liked, but it's what our schedule allowed). We then wandered around the central area, stopped for apertivo, wandered around some more, had dinner, etc. We really had no issues with being too tired (I think we were really excited, which was perfect) -- I was concerned about that but it was not a problem at all.
The next day we visited Centro Storico and LOVED it. It really, really helped with centering the geography and history of the city. If we'd had time for a tour we would have done so. We then caught a 2pm train to Lago Orta. By this afternoon we were tired :).
I'm not a fan of cramming in all the big things when I visit a place. If that means I only see one big thing, then that's how it goes. I'd much rather have more leisure to just walk around or visit a park or linger looking at buildings or artwork. But that's ME. Other people are very different. So I'd figure out what do you REALLY want to do and/or see in either or both of these cities and then plan around that.
We're planning a trip to Rome (and Puglia) for next May and will be in Rome 3 nights (2.5 days). There's no way we can see all the things and I'm realizing that again I'd rather do a walking tour and definitely visit the Borghese Gallery to see Bernini over a Colosseum visit, if I have to choose.
Carrie