I have had the Gear Fit for a couple of days now, and it works seamlessly with the Note 3.
I tried the previous Gear once (the new ones are more or less the same size), and it was simply a bit too large and clunky for me even though I would like the extra functionality (voice search, camera, using it for phone calls, IR-blaster that can control your TV and so on) that it offers.
The Fit is more basic, but you get notifications when e-mails, texts and phone calls arrive. You can also control media playback and volume (Spotify, podcasts, the regular music player and so on) from it, which is a good thing.
The heart rate monitor seems to work well, the step counter is a bit off and counts rather optimistically. I have seen this mentioned in several reviews, and it will probably be adjusted in an update. After all, counting steps from a device mounted on your arm is probably quite a challenge since the amount of arm motion when walking differs a lot from person to person. The ideal solution would of course be to calibrate it to each person in some way - e.g.: "touch to start calibrating and then walk 100 steps in your usual manner"
All in all the Fit is a cool little device - and it looks great as well with the curved screen.