There are some differences between MainStage and Ableton - but you can use either software to create a great live keys rig. There are videos in this article to help you decide which software is best as well as choose a computer to use!
Both versions of Sunday Keys are built from the ground up so they have their own presets and patches. You'll want to consider what you are wanting to use the template for. Ableton is a bit better when it comes to CPU usage and stability, also you can run tracks with much more customization in Ableton. MainStage has a really neat visual layout that makes it super easy (and fun) to use the template. The two also cannot share patches, there are completely separate sounds and presets for each platform.
Check out this video to learn about more about setting up an Ableton Live Keys Rig and some differences between MainStage and Ableton Live:
Check out this video to help choose which version of Ableton Live you need:
Check out this video for more about setting up a live keys rig: