It's theoretically possible that someone could put together a website that serves up photos the exact pixel-dimentions as the viewing device and, thus, a larger screen would get a larger photo.
And it's also possible that some software will decide to give you desktop sites instead of mobile sites based on the size of your device.
But I consider both of those to be pretty unlikely. In all likelihood you'll be downloading and viewing the exact same content as you would on a smaller phone, you'd just be scrolling less to see it all.
I think this boils down to behavior. With my older iPhones, I tend to use mobile sites while on the 6 Plus, I'm using desktop versions more often. The bigger screen is also more conducive to streaming videos.