We rented a car last year in Italy. My dad (USC) and I were named drivers.
I had both my UK and US licences with me because I wasn't sure which they'd prefer. The rental car guy asked where I was living and when I said UK, he suggested using my US licence for the rental.
His logic: if I got a ticket or was in an accident in the rental, any points would go on the licence I don't use regularly, so wouldn't affect insurance or anything. In Europe, they'd also be less likely to chase up a US driver to get points on a licence than they would a UK driver. I'm not sure how that works, but that's what he said.
I have also heard that when booking a rental online, sometimes prices are different depending on what country the driver's licence is from, so it might be worth playing around if you're booking ahead of time.