Turns out things might have changed, if the sources in the other answers once were right.
The differences are these:
- Better seats in a 1+2 configuration.
- Dedicated 1st class conductor.
- All cars are closer to the restaurant car.
- More storage space.
- Less noise (most likely).
- Generally better WC access and state.
- Faster boarding.
The 1+2 configuration is used cleverly by the booking system and solo passengers will get a solo seat, dual passengers will get seats facing each other in the 1 row when available and the quad seating will be left for groups of 3 or 4.
What's not included is complimentary drinks and snacks. I was a bit disappointed when I found this out. There's also no lounge access included nor fast track.
Source: travelled with Frecciabianca 1st class when writing this answer and talked with the restaurant staff.