To answer your question regarding What MainStage will give you over iTunes - You don't go into details about what equipment you are using for your performances but Mainstage will allow you to have a separate patch for each song with a multitude of different variables available.
So for example when you perform song A with its backing track, you may have a chorus effect on your guitar and a flange on your vocal channel. Then when that song is over you hit a button and the next patch loads with a different backing track and this time with distortion in the guitar sound and chorus on the vocals. Song 3 has a different backing track but this time you are accompanying it with a two layered keyboard sound, all preloaded on that patch.
As a performance tool main stage is vastly superior to iTunes and of course is based in Logic so you will be very familiar with it.
Regarding performing, I have main stage set up with half the screen showing channel strip settings including volume etc, and the other half with the lyrics / chords notes needed for performing. Much tidier than scraps of paper!
Hope it helps.