First early impressions so far.
The screen is far and above the most beautiful screen on a phone I've ever seen. It's very responsive and able to pick up your touch with your finger not even touching it. In my eyes it's the best screen of any phone I've worked with.
When I open up an app, it's open. Now. There's no waiting. Unless the app has pages set there purposely while it loads like many games will. Those aside it will instantly load into an app with no issues. I enjoy the multi task ability it has with apps as well, the screen size and the way they have it set up compared to the previous notes make it look and feel less clunky.
Camera is pretty crisp, I've not taken too many photos with it but the ones I have seem pretty nice and the focus is improved over what was my S3. It's instant from when you push the photo button to when it takes the photo as well, which is nice as my S3 for some reason at times would go completely out of focus then refocus at random when I took pictures sometimes.
I got the phone at 3pm on Friday and didn't have to put it on the charger until Saturday night around 10pm. This time frame included light to moderate phone useage and heavy browsing and light game play.
While I haven't played music or watched video on it yet, it seems my normal ring tones I had from my previous phone aren't as loud on this. It may be because of the speaker location. On the Note 3 it's located on the bottom of the phone next to the charging port as opposed to the back ph the phone. I always set my phone screen side down (case protected the screen) with the speaker facing up so it was easier to hear it ring I suppose. It's definitely louder while holding it though compared to my old and most phones.
I wasn't aware the charging cable wasn't micro USB...though the large phone, that makes sense I guess. Stinks I'll have to buy 1 or two more chargers for it eventually.
Will post more as I use it more and will answer any questions about it you guys post.