FIUMICINO AEROPORTO - ROMA TIBURTINA:
Aboard a regional train that makes multiple stops. Takes 48 min and costs only 8€.
So with this solution the total train time is:
Fiumicino - Tiburtina: 48 min
Tiburtina - Firenze: 82 min
Total time: 130 min (plus train change time at Tiburtina)
Total price to Florence (standard at full base fare): 8+45=53€
FIUMICINO AEROPORTO - ROMA TERMINI
Aboard the Leonardo Express. Makes no stops. Takes 32 minutes and costs 14€.
Fiumicino - Termini: 32 min
Termini - Tiburtina: 9 min
Tiburtina - Firenze: 82 min
Total time: 123 min (plus train change time at Termini)
Total price to Florence (standard at full base fare): 14+45=59€
The only difference is therefore the price, because now all trains to Florence stop at both Termini and Tiburtina, therefore no matter which solution you choose, you will likely board the same Freccia train, whether you pick it up at Termini (with the Leonardo Express) or at Tiburtina (with the slower Regional train).
www.trenitalia.com
enter
From: FIUMICINO AEROPORTO
To: FIRENZE S.M. NOVELLA
I also think that at Tiburtina you are less likely to be robbed by the gypsies. More modern too, after the renovation a few years ago.