I came from the Note 2, but have used my friends' Note 3's extensively. Phone is really nice, the build quality, responsiveness, battery life, and stability are all nice. I did have a problem with my GPS in that it couldn't find my location once but restarting the phone fixed it. However, I will point out that the Note 2 and 3 are better for two handed texting, and the Z2 is great for 1 handed swyping. The speaker phone, because of the water proofing, is quieter and not as clear on the note 2, but has comparable quality to the note 3 speaker (although note 3 is louder). Z2 does get points for front facing speakers though, but flipping the note 2 face down while on speaker gave both parties better results.
Using the Neutron music app, (disgusting UI, but the BEST in sound quality) I found that the note 2 has better sound quality. There is a slight background noise, but that is diminished with moderate volume. Through hi-fi headphones, the note 2 has a better lows, the bass hits harder, with no bleed into the mid or high range. The Z2 has a bit of a bright but overall balanced sound. If you are a basshead then the note 2 is more preferable/fun to listen to but the Z2 is cleaner.
As for the UI, Sony has done a great job with keeping everything simple and clean. It's fast, responsive, and I have had no problems with lagging or hang ups. However, Samsung gives you more customization and even though it feels bloated some times, it lets me do what I need quickly and easily. Like changing the vibration intensity, blocking calls with acceptations, changing brightness in the notification area w/o going to the second tab, tapping the brightness icon, and then changing it. Stock Sony is limited, like stock Android.
Notification light under the speaker is sweet, I just wish it could be a little brighter/customizable. Screen is smaller and easier to reach across, but is lightly mitigated by the bezel size and ergonomics. The blacks are REALLY good for an IPS screen, and I don't notice much of a difference from the true blacks on the AMOLED screen, the colors are accurate yet still vibrant, which is great. The one thing lacking on the Sony screen is the viewing angles, which are OK and the screen is kinda reflective, but I can still see if I max the brightness under the brightest day.