Maybe by Fallout 8, the East and West will meet in the middle, and then it might matter. Especially if the two sides start using Institute and Shi technology, it may happen all the faster. The minute men are sweet little kids, sure, but I don't want them being the only ones in between the commonwealth and the legion.
Short term, I think the choice for the commonwealth is easy. Only the Minutemen genuinely care. Long term, it gets complicated.

@Sirdanest I doubt it. There will be too many role playing factors to consider from every game. Who did what on each coast? Who lived and who died? There are too many variables.

There were an incredible number of possible endings for Fallout 1 and 2, and yet a canon ending for many of those variables has been chosen. There definitely aren't too many variables this time around, and they're probably going to have to start deciding on who won what sooner or later for both coasts anyway. Unless Bethesda just decides to never let us ever see the west coast again.

In my personal opinion i think overall the minuteman would be the best for the Commonwealth.
they dont tolerate injustice and will protect the people,but honestly i think at the end they will fail as they are following a society like the one in the old world (Like the NCR) and unlike there is some revolution or something they re  are bound to make the same mistakes.

The railroad only cares about synths and are not really rulers so they will get replaced by another faction pretty quickly.

BOS only cares about technology tough so i dont think much will change and at the end they will split, i mean look at veronica and the outcast.

the institute is a good choice tough because the player decides how it will be, pretty much like independent new vegas but not so free.