Looing back on my past travel with AA I can think of MANY instances where if not for MRTC I'd have chosen another carrier.

LGA-MCO: I'd have chosen jetBlue because they fly from JFK and JFK is almost next door to me. Hell, since I was going to Atlanta anyway I'd have just taken DL straight ftom NY instead of transfering to them in MCO.

JFK-MIA-MAD: I went via MIA (y'all know the hell that is) when I could have flewn Iberia or Delta nonstop. Also a large portion of my travel group took DL and I'd have rather went with them if not for MRTC.

JFK-MIA-EZE: A plethora of options. UA, Souther Winds, Aerolineas, Lan Chile (to name a few). Since I was willing to pull one stop I could have done it ANYWHERE. Plus my frends took Aerolineas so I'd have been better on it.

JFK-SFO: With E+ UA would win my ticket.

JFK-LHR: Air India was cheaper, but since I was going to Dublin I could have taken Aer Lingus as well for super-cheap.