Tuscany vs Amalfi Coast, Late November

The Amalfi Coast itself, in November, would probably not be particularly enjoyable.
The Campania region in general however, with Pompeii, Herculaneum, Paestum and also Naples, would have plenty of history, especially Roman history, to offer.
North of Rome, Tuscany and Umbria will also have plenty of historical sights to see. Florence in particular, but also smaller towns like Siena, Arezzo, Assisi.
It's hard to make a choice between going north or south. Both have plenty of worthwhile things to see and do.
You may not need to rent a car at all. Certainly not to visit Rome, Florence, or Naples/Pompeii. The train is a much better choice to visit Italian cities and towns. The car could be helpful to visit the Tuscan countryside, but I'm not sure the countryside would be a place to go in November. That time of the year, I'd stick to cities and towns, where there are plenty of things to see even with less amenable weather.
In late November the weather will be likely cold, meaning low 50s during the day and low 40s at night. Gray or rainy skies, with short daylight hours will be the norm. I would not count on significant differences between Naples, Rome, or Florence. You should expect temperatures in the above range with less than 5 F degrees variances between those cities.

I've visited Tuscany and Campania a couple of times in February, but never in November. I suspect that weather would be similar but days a little shorter. The weather was mild, with some rain, some overcast days, and some balmy, sunny days as well. You can get a better idea of actual weather by going to this site (Paris is the default location) and following the ""past weather" link. That will give you daily conditions for the last several years.

For both history and natural beauty, I'd choose Campania. Several years ago I stayed in Sorrento and day tripped to Naples, Herculaneum and Pompeii on the local Circumvesuviana train. There is regular ferry service to Capri and buses to the Amalfi Coast towns. This year, I stayed in Salerno, rented a car and drove the Amalfi Coast and to Paestum. If you want adventure - driving the AC will do it. Here's my "report." I enjoyed my stays in both towns. Salerno's prices are lower and it has more sights - and the food is just as good. It's also at sea level - the old town is just meters from the sea. The old town of Sorrento is up on the hill, so to get down to the sea, you have a lot of stairs. But you can get better views from up high. Salerno is closer to the AC towns. The scenic coast is from Salerno to Positano. The road from Positano to Sorrento is almost all inland. It's also possible to take the buses from Salerno to the AC towns if the driving is too much for you. Do park the car in Amalfi Town and take the bus up to Ravello.

I took the fast train from Rome to Salerno and rented (and returned) a car there.