The potential of Liberty Prime plus their air superiority and power armor supply makes them a formidable force. The Institute has the most defensible position and, therefore, wins almost all engagements on its own turf and repels almost every direct attack attempt. But if put on a level playing field, the Brotherhood is more well prepared for a military engagement. The Institute mostly relies on secrecy, infiltration, and small-scale operations.
The Minutemen have good numbers, but too little infrastructure. The Railroad is admirable, but they operate on the same level as the Institute and would be crushed in direct engagements.
I went with the (so far unpopular choice) Railroad because I liked the whole "underdog" aspect; a bunch of rabble with noble (and arguably misguided) intentions taking on a huge organization... and actually succeeding.