home base: Rome or Florence?

The advantage would only be based on the areas you want to visit. The areas are far enough apart that to do both would not allow day trips from one region easily to the the other. Either focus on one or plan a "home base" in each. That said, If I had to choose, basing in Florence probably offers more options by Bus and Train (Siena, Assisi, Bolonga, Pisa, other Tuscan cities) and maybe even some other Northern Italian destinations either as a day trip or overnight. Rome has it's charms too (I like Rome more than any other Italian city) but mostly in Rome then a few destination close including some stops in Umbria.

There are not equal. What day trips do you want to do? That will dictate the base. Florence is much small and access to the train station a little easier depending on where you would stay in Florence (obviously the same for Rome). Rome with multi train station and lines would have more train options.

If you have 10 days, why not split it between the two cities? 5 in each? That way you can explore south and west, from Rome, and North and east from Florence.

If you are in Florence, you have easier access to do day trips to Siena, Pisa, Lucca, Venice, Bologna, etc. From Rome you can spend a good 3 days just in Rome, then do a trip to Pompeii (although that would be a bit easier from Sorrento) Assisi, Orvieto.

If I had 10 days, I would split between the 2 cities.

I agree with Ellen, if you can split the time, do that. There are dozens of daytrip options from either Firenze or Roma.

I'd absolutely split your time between both cities. There's too much to see in Rome to try and do over mutiple day trips from Florence and you'll waste too much sightseeing time and $$ on transport: 90 minutes OW, 3 hours RT. The same is true in reverse for trying to cover Tuscany from Rome, and you'll want a couple of days for Florence itself.

If day trips are in the plan, they'll be much quicker and easier to do from the nearest city. I'd also highly recommend flying into one and out of the other to eliminate backtracking.

jpolanski,

I agree that 5 nights in each city is better. There is so much to see you will get to see the highlights from each city in that time.
Staying in just one as a base you will spend too much time traveling. Fly into one stay 5 nights, train to the other for 5 nights and fly home from there. Enjoy.

Lorie

They are too far apart. You need to split your stay into 2 bases (Florence, Rome). How to allocate the time depends on what you want to see from each. Remember that 3 nights in one place is actually only 2 full days in that place.
If you can't find a reasonable open jaw (fly to Florence and return from Rome, or viceversa), you can fly in and out of Rome. In that case it is more efficient to go to Florence first by train on the day you land in Rome, then return to Rome for the last days of your trip. That way you save one hotel change.