My experience is Florence in 2010 (4 nights/hotel) and 2015 (5 nights/apartment), and Rome in 2010 (2 nights/hotel) and 2017 (6 nights/apartment).
I am glad I don't really have to pick between the two. Florence--especially in 2015--was wonderful in that everything is walkable, and it almost seems like a small town. Very focused on Renaissance history and art. Felt a little touristy. Picturesque & charming.
But we just got back from Rome. You have to work to get Rome. You get your maps, buy your bus passes, and integrate your life with normal Romans living their lives in order to fully appreciate this place. We were there earlier this month, and it didn't seem that touristy at all, except at the usual culprits like Spanish Steps and Trevi Fountain, which we saw for a few minutes, then moved on.
While there was tons to do and see within walking distance of our apartment at Campo de' Fiori, we got a much better perspective by taking advantage of the buses and Metro to span the city & see the 'layers of history', as the above poster says. We viewed artifacts from the early Iron Age, 1000 B.C., at a museum within the Baths of Diocletian, which is right next to the Roma Termini train station. People walking right by like it's a petrol station! Then you take the bus up north of Porta Pia to a nondescript-from-the-outside church of St. Costanza, where there was beautiful 4th century mosaic. And not far from there is Villa Torlonia, with the somewhat-dilapidated wartime home of Mussolini. Simply amazing, all off the tourist radar.
And...I think the food in Rome has Florence beat, although I think that's saying a lot as Firenze has great food, street food in particular. But to my way of thinking there is more variety in Italian cuisines in Rome. Traditional Roman fare is wonderful, but we also sampled Sicilian as well as Puglian dishes--fantastic. Also, I really dug having my early morning caffe at a little tabacchi shop bar. By the second day the barrister nodded to me, knowing what I wanted. No fanfare, just doing business. Loved it!