To me, assuming a 4.7" phone, neither keeping the same resolution (leading to 277 ppi) or doubling it (555 ppi) make any sense. First would be pixely, second would be super expensive and pointless (200ish ppi more than necessary).
I bet they do whatever resolution that would give roughly the same ppi they have now (1080p?) and tell devs to deal with it, and they will. There would be black bars all around, but that won't last long ala the 4" change, and then Apple will be set for the long haul since there probably won't be any screen size change for a very long time, if ever again. Apple has made way bigger changes for devs before (OS X, Intel) and similar ones (iPhone 4S --> 5) before too, after all.
I bet they do whatever resolution that would give roughly the same ppi they have now (1080p?) and tell devs to deal with it, and they will. There would be black bars all around, but that won't last long ala the 4" change, and then Apple will be set for the long haul since there probably won't be any screen size change for a very long time, if ever again. Apple has made way bigger changes for devs before (OS X, Intel) and similar ones (iPhone 4S --> 5) before too, after all.