I prefer medium. Price and battery life aren't part of my decision. Cameras, on the other hand, are a consideration, but you didn't mention that. But let's stick with the assumption that you did - equal battery life, equal cameras, equal price, equal CPU/GPU, equal biometrics, equal AR/VR, equal ports... I prefer medium.
"All other things being equal, which screen size do you prefer?" A simple question that would have produced the same results. But like they say, "All things being equal, which they never are." If I needed longer battery life I'd certainly expect that a larger phone would offer longer battery life. I'd be quite unhappy if it didn't.