I have flown both 737 and 757 as a line pilot, and held TRE on both; on line I've flown go arounds in both types with and without the autopilot. On line I've never had a bad experience but it has been my habit for many years to brief not only the pattern but the physical actions of the go around, and encourage the F.O. to do the same.
By hand or by autopilot it is not a difficult thing on either aircraft, but if you haven't thought it through the startle factor has the potential to make it difficult to manage correctly. I have watched 2 TREs botch an all engines go around in the sim when they went around having expected to land off an approach, they wouldn't have damaged anything but it wasn't pretty.
Anyone can get it wrong, dealing with the stress after that can be very difficult.