I don't have a Verizon version but I do have the Sprint version and after 4 days of use I feel like it's safe to say that the Note 2 has a better radio than the Note 3. As far as comparing decibels, I use Sensorly and my Note 2 always floated around the -107 area, sometimes better, sometimes worse. The Note 3 shows -110 or 111 much more frequently than the Note 2 did. Performance wise though, I can't really tell the difference. There are just too many variables. Last Sunday I was at my moms friends house and my buddy with his HTC One and my other friend with his Galaxy S4 (both on Sprint) were there too (was my bday!
). We tested the Wifi and the HTC One won by a big margin. The connection at that house is around 10 MBits, we were one wall removed from the router and the HTC One got between 7 and 8 MBit whereas the GS4 consistently beat the Note 3 by a small margin averaging around 3 MBit.
I consider all these non scientific tests, and too me the difference in performance when not looking at Sensoryly or SpeedTest, between the Note 2 and 3 are not discernible. Also, the longer I use the phone, the better it seems to get, as if it slowly got to know its surroundings at what towers to hook up to. Would I return this phone and go back to the Note 2 or even the HTC One? Not a chance. I haven't had a dropped call, internet performance seems on par, and the whole phone just is so much faster than the Note 2 (Google Earth has never looked this smooth), add to that the new useful features and the much better screen along with the much better feeling hardware, and the Note 3 is a keeper in my book.
I know, it's Sprint vs Verizon version....but look at it this way, if I can live with and get pretty decent speeds on Sprint, you Verizon guys shouldn't have any problems.
Edit: And just as I finished posting this, the phone dropped down to 3G after getting 6 MBit on a Speedtest just a few minutes prior. I must say...I haven't seen the 3G symbol at my house in quite a long time, and I unfortunately get to see more of it here with the Note 3. Again....I never had stellar signal at my house to begin with, so I am using Wifi again, and it works fine in other areas I frequent. So yes, the radio is worse, I am not happy about it, but the rest of the phone is worth it. Maybe they will push a software update to make it better?