Here's where Apple's resistance to larger screens (and bigger smartphones) also bites them: Larger phones can pack much larger batteries, leading to longer battery life (even despite the larger display, which does _not_ consume proportionally more energy). E.g. a Note II will last nearly two full days without a recharge, and you can get 2.5 days of normal use with power savings enabled.
My own experience with Galaxy Mega (5.8) is awful. Its screen is huge; coming from an iPhone 4S yet its battery is terrible; barely last a day (7am til 6pm) with a full recharge.