I would totally recommend to stay at Fabrizio's flat. It was the perfect cosy spot to relax after long days of visiting the sights of rome. Trastevere is one of my favourite quarters in rome, it's a cool area, close to everything (walking distance!!), many restaurants, bars and just cool places to have a coffee and enjoy the italian way of life :)
Fab is a perfect host, I have been to many places with Airbnb and this was one of the best experiences so far! Fast answers, easy to find instructions, really comforting and the flat is well equipped (breakfast supplies, coffee machine etc...), you feel totally like you are in a second home. Also the bed was more than comfortable and the heating worked perfectly (very important when you're staying in italy in december).
So all in all: 100% recommendation!!!