I decided to make the transition from the Note 3 to the M8. I honestly can't begin to describe how happy I am with this phone.
The only noticeable difference for me in the display is when viewing the color black. On the Note 3's display, black is just turned off pixels, so it's a true black (kinda miss that). In every other regard, I think the displays are comparable.
The M8 is definitely faster than the Note 3 IMO. Touchwiz was so bloated and laggy, whereas Sense seems more lightweight and optimized. Apps open faster and the overall performance is beter.
Surprisingly, I don't notice much of a difference in battery life. HTC must have really optimized their software in this device because it seems about the same as the Note 3.
The camera is the main downfall of this phone, but not a huge one. I really enjoyed the Note 3's camera quality and took it for granted. The M8's camera isn't bad, but the quality just doesn't compare except for when using the front facing camera. There is a plethora of options available in the camera app, though, so having the features shouldn't be a problem.
To wrap this up, I'll just say that boom sound is amazing (seriously the best speakers I've ever had in a mobile device), I've never used Zoe, and my experience with the IR blaster has been about the same as with the Note 3
HTC One M8 (Current): Stock / 4.4.2 KK
Samsung Galaxy Note 3 (Retired): Omega v12 / 4.4.2 KK
Samsung Galaxy S4 (Sold): Stock Unrooted MF3 / 4.2.2 JB
Samsung Galaxy S3 (Retired): STOCKORAMA V2.0 / 4.1.2 JB
Samsung Galaxy S2 E4GT (Retired): Stock GB27 / 4.1.2 JB
HTC EVO 3D (Retired): Team PkmN - Charmander 4.2.0 / 4.0.3 ICS
HTC Droid Incredible 2 (Retired): Virtuous Unity v2.39.0 / 2.3.4 GB
HTC Hero (Retired): TeamHeroC / 2.3.7 GB