Suggestions on new phone from note 3?

So I want to upgrade from my note 3 I think, but not really sure what out there would be a good upgrade. A must is the phone has to be rootable, preferably bootloader unlocked. I wouldnt mind something like the Nexus 6p where I could use the same phone on maybe sprint, but I want to make sure Im making the best fiscal decision. I do enjoy the s-pen a lot, but I know the note 5 has no root or unlocked bootloader. So what would be a phone where I would see improved battery life/snapiness of the phone, as well as better signal (I notice that newer iPhones my family have get great signal when Im getting very poor, so thinking it may have to do with older phone). Would love some help

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