Honestly, I've had both devices.
Battery Life: Note 4 will kick ass. But the S6 is not half as bad as the media makes it out to be. Very decent, better than the S5's battery, even though it's smaller, with more power hungry internals. Just shows you what some optimizations can do. If you want to keep the S6 forever, you might have a problem with replacing the battery. But the S6 have fast charging. And not the Note 4's fast charging, it's SUPER fast, like seriously. It charges wirelessly about as fast as the Note 4. O yes, wireless. Built in madafaka!
Screen: Both have a fantastic screen, S6 screen is a little better just because of the size, the PPI goes up. If you get the edge, even better. The curved edges gives the illusion of an edge to edge screen on the sides.
Build Quality: S6 hands down. Not that the theirs anything wrong with the Note 4's build, the S6 just made it better. The Note 4 felt good in hand when I first upgraded from the S5, but the S6 just so much more. Because of the thin sides it also feelz like the phone is a lot thinner than what it really is.
Size: Bigger is better? Sometimes. But sliding the S6edge into my pocket is soooo much easier, and taking it out while sitting down. But if you use your phone for gaming... get the Note 4.
Software: The S6's touchwiz is better the Note 4, it has a themeing engine, if that's important to you... buttery smooth (even more than the note 4)
Storage: The Note 4 was a 32GB, and I had a 32gb sd card. Now I have a 64gb phone. Internal storage is sooo much faster than the SD card.
Camera: How do you make a awesome camera better? No idea, but they did it with the S6. So fast, so lightweight, so good in the dark.
Anything else you want to know, just ask me. Someone who have owned both phones
