MainStage has a few features that logic does not have for live performance ,which MOST people will benefit from. The biggest thing is that you can setup a set list of patches and instantly change patches via program change command, with each patch being whatever mixer config you want with instruments, sounds, audio strips or whatever you want. For most people, I think that is the way to go for using software instruments on stage.
That being said, for live playback of backing tracks, it starts to get murkier. As you get more complicated, MainStage can't really handle it...then you'd be better off in LogicPro, but you'll lose the Patch setlist capability, which for me is major.
My advise is to keep your backing track playback as simple as possible. Just record your backing tracks as MP3's fully mixed and let them playback from somewhere. MainStage can handle that, and if it can't, you can always just put them on an iPod and hit play from there. Simple. Don't mess with midi sequence playback on stage. Its a fools errand in my opinion. You can always record a click track MP3 also and send that to the drummer or whatever.
If you somehow need to insist on being able to do advanced created things in the sequencer in a live setting, then definitely go LogicPro because MainStage's playback capabilities are rudimentary and sometimes flukey to figure out, but personally I would would avoid doing that kind of stuff live. Keep the setup simple.
As far as being able to use software and hardware synths to play on... (not midi sequencing), that can all be handled by either product, but I just think its easier to setup a setlist of songs in MainStage...where you can send it a program change and have all your software instruments and external synths change to the right sound, etc.. MainStage is perfect for that and LogicPro is not, then you have to jump through hoops in LogicPro and do complicated environment setups to try to achieve stuff like that.. so pick your poison...
5,1 MacPro 3.46ghz x 12 128gb ram, OSX 10.14, Logic Pro 10.4.8, Mainstage3, Cubase10, StudioOne, Reaper, DP9, VEP, VSL, too many plugins to list