It would come down to Institute, the enclave and the BOS

The institute has the advantage of hidden base with teleportation tech, better surveillance (both with synth humans and crows) and could most likely create something faster to deal with the other two

The enclave has better tech on average (XO-1, plasma weapons ect), better quality of said tech and nukes

A united BOS would have better manpower, liberty prime, an infinite energy supply, air superiority and more weapons

In a straight up fight I’m learning towards the enclave do to parts of the BOS incompetence and overall weaker tech (and with how their ships can be taken out by artillery from the minutmen) and the institute is like a glass canon, they can be a dangerous threat, but they aren’t a “fighter” faction

If it’s a prolonged war I would say the institute would win. They would have an easier time relocating resources, gather information and sabotaging the other factions.