Hello! You would be missing a removable battery and some sturdiness. The S7E screen is 5.5 in. I can't remember if that is smaller or the same as the Note 3. I think in most areas, you'll find the S7E to be a solid upgrade.
Well worth the switch Samsung did a great job with this device I can't believe the screen is the same size as the iPhone plus but the foot print is smaller. Coming from the 6s this phone is years ahead in all ways.
You wouldn't be missing much. I came from a Note 2, Note 5, Note 7 before I got the S7E and I'm really happy with it. I miss the s-pen, but I downloaded S-Notes from the galaxy app store and bought a little stylus - so that fixed my s-pen problems