I do have Lte and the Note 2, as well as the S3. N2 is way better hands down. My house is on the outside edge of a signal. (-106 to -111 RSRP and very high SNR) The S3 once in a while picked it up and jumps on and off, on and off... keeping my data in limbo. sucks big balls. The note 2, I walk out side and it grabs within seconds and holds. N2 seems a little quicker on the web under 3G. I can set both my S3, my Wife's, and The N2 next to each other and the N2 Wins every time. Holding both and going outside. N2 will switch and when ever the S3 gets it, its not holding it. In a good Lte area but at the edge of the map. Example, Texas Motor Speed way. N2 will have already switch and the S3 might have?... Nope, oh but my wife's S3 did... (5 mins later) There it is. You can never tell unless you cycle it. BUT, if your in an area like southern Keller, TX. That has real good coverage, they all work fine it seems. A big deal is the note doesn't jump on and off over and over when its right at that point of getting it.
If feels like the S3 isn't as strong but the threshold is to high. Where the Note is stronger with the same threshold. a lot smoother switch between 3G and 4G on the N2 as well. Also I have a real had time getting Wimax 4G with either of them. Thought they would fix that on the N2.