For whatever reason, it used to be very easy to have your contact photos show up full screen on the iPhone when a particular contact called. And then, a few versions back, it just seemed to stop working.
This iMore thread explains how to get it back. Basically, just make sure that the picture you choose for your contact fills up the whole screen, even as you pick the little circle version that show up around the OS.
It’s a small thing, but it’s really nice to have full screen photos on the big iPhone 6S screen.