Biggest differences between this and the Note7 are the physical size, and the lack of the S Pen.
Biggest reason I got the Note 7 was because of the ability to scribble down all the notes I needed at work. This phone does not have S Pen support, but with the S Note app, you can still jot down notes and such, but you scribble with the tip of your finger or any stylus that works with it...the Note had a dock for the pen, so any stylus you pick up to use with this phone has the potential to go missing between uses.
The size of the S7 Edge screen is 5.5 in, Note 7 is 5.7 in, so there will be a visible difference in size of the phone. The Note has squared corners while the Edge is more rounded. Otherwise, the software and firmware is pretty well the same. If there are minor differences in the little bits and bobs of the phone, they are minimal.