Here's why I switched to and kept the iPhone 6+ over the Galaxy Note 3 (not in any order):
1. TouchID: It's really nice not having to type a passcode for your lockscreen while still having it locked so no one can get on. Same thing when downloading apps.
2. Camera: This was huge for me. I was always annoyed with my Note 3 camera. After using the 6+ camera, I can easily say it's better than any camera I've ever used on any phone and better than any point-and-shoot camera I've used. The low light performance absolutely blows me away. I can't express how much happier I am with it than the Note 3's.
3. Connectivity: I've always missed iMessage, emojis, ease of syncing with iTunes, FaceTime, etc. since I switched back to Android from an iPhone. Also, everything just works with the iPhone, as many people have said before. I didn't really find myself customizing with Android as much as I thought I would and really just got to the point where I wanted a great overall phone.
4. iOS 8/Yosemite: The fact that Apple is starting to push the boundaries on their locked ecosystem made me want to switch as well. For example, third party keyboards and app interactions. Handoff made me want to switch as well since I'd be able to get calls, messages, etc. on my Macs and "hand websites off" from one device to the next.
5. Design: The Galaxy Note 3 lacks design imo. The software overall is outdated, not consistent, cluttered, and just overall doesn't look that great. The design on the outside isn't bad looking but isn't very premium. Plus just the divide between Samsung/Android. iPhone is the complete opposite. Design is beautiful, fresh, consistent throughout, and clean. The actual hardware design is stunning and very "premium" imo. I actually had to say "wow" when I took it out of the box, it amazed me so much. Apple has complete control over the hardware and software so everything is designed to work together and efficiently.
6. Screen: Best screen I've used on a mobile device period. I can't get over how well it does in direct sunlight either. The clarity and quality is unbelievable.
7. Battery: I was amazed at how much better the battery on the 6+ is compared to the 4S and Note 3 I had. Note 3 was better than the 4S but 6+ far exceeds both. This will be different if you get the regular 6 though.
The reasons I switched are pretty minor, as my Note 3 still performs great, but it was enough to make me switch.
This. I just came from an HTC M8. Although it rivals the 6 in terms of build quality and physical aesthetics, the rest of it just doesn't hold a candle for the above reasons.