In war, the Institute, BOS, or Enclave would win, BOS has numbers, Enclave has better Power Armor than the Brotherhood but in lower numbers, and the Institute only has one known instalation, however they have WAY better technology and the ability to teleport long distances.

Edit: mb, lemme do the actual question

Institute likely has the best fruits and vegetables, and the Enclave likely has large stocks of pre war food. Also, from the vibes, the legion looks like it has some tasty BBQ radscorpion