Like many on the message board, I was fortunate to fly both RR and PW 2037 powered 757s. The starting sequences as mentioned are different. RB211 starts like a car engine. The Pratts have a lower max motoring, but you can go to the back make lunch and come back before the Pratts get to idle speed.
The Pratts have a lot of residual thrust at idle, so landing and taxiing can be pretty much done at idle thrust. The Rolls on the other hand require just a little bit of juice to taxi them and the same for landing.
The two engines have distinctly different sounds when in reverse and on takeoff power.
And from above, American's Fleet are RR powered. When they bought the assets of TWA, they acquired 27 very new 757s (PW 2037) and I believe have all but gotten rid of them. Some went to Pegasus leasing, whereas I flew 708/715/720TW while at TransMeridian. The other half, of course will be headed to Atlanta with DL.