Fat Boy has a much more "upright" sitting position and may be more comfortable for the average rider on longer rides. The Breakout has the 117 engine, bigger than the FB's 114. ABS is standard on the Breakout, and optional on the FB. Traction control is an additional option on the Breakout. Cruise control is standard on both.
From there, it's a styling and handling preference for the buyer. The Fat Boy is a little more cumbersome (IMHO) due to the fat tire in front. The Breakout has this whole, "hot-rod" vibe about it and I like it better.
Honestly I find the Breakout to be much better looking, the wheels really do stand out. Speaking of wheels, I really did not like the change the Fat Boy. Feature and price wise the Breakout is a steal. If you want the Anniversary paint then you will need a Fat Boy
Breakout is now my fav Softail…at least for new bikes. It sort of has the Pro Street look…wheels are amazing for stock. I could see myself buying one and doing a 131 Stage IV on it.