I have recently been rated on the B787 off an A320, so here are a few things i have noticed:
B: F/D's need to be switched back on after G/A from Visual app, otherwise they disappear at accel ht.
A: FD's come back on and stay on
B: GA is done at 2000fpm, unless TOGA pressed again, then it is full rated
A: GA is at full rated thrust
B: after GA, approach needs to be restrung
A: Approach is restrung automatically (and ALTN route offered)
B: Auto throttle wake up won't always stop you from getting too slow
A: Alpha floor will always protect you (unless you have an abnormal flight control law downgrade)
B: you can stall
A: You can't stall (unless you have an abnormal flight control law downgrade)
B: you can't string an alternate after the missed approach, (at the end of the flight plan, therefore no really accurate fuel predictions at the alternate)
A: you CAN string an alternate after the missed approach, (at the end of the flight plan, this will give you accurate fuel predictions to the alternate)
B: Auto rudder trim with sensed Engine failure (AP not required)
A: Rudder trim required until AP in
B: Non normal checklists are much better, includes all the FCOM notes
A: ECAM doesn't totally fix the problem, you still need to look in the FCOM if time permits
B: F*@#en HDG Bug

A: Hdg Bug disappears when in NAV
B: DCT, then select LNAV
A: DCT to then NAV automatically engages
B: Automatic Anti Ice (i believe this is 777/787 only)
A: Manual Anti Ice
B: no times/dist on LEGS page (requires pushing next page)
A: times/dist on Flt Pln page
B: no distance to threshold (except fix page)
A: PROG page gives distance to threshold, or any wpt
B: the box

A: THE BOX
these are the big items i see day to day. my favourite???
I only do 1 sector in the B787 (used to do 4 in the A320)
I go to nice places in the B787, I always ended up at home in the A320
I feel you program the Airbus, then let it go, the Boeing, you have to keep pressing a button to keep it flying.