Bought a GN on launch day, back in 2011 or whatever it was.
GN was a decent device overall. Battery life was a total joke, even on Samsung's extended battery.
Signal strength was ALWAYS an issue.
Bought a Note 3 10/10, launch day for Verizon network.
I can tell you that the N3 is superior in nearly every regard to the GN. As much as I have always defended the GN, in retrospect (and now in comparison) it becomes harder to do so, when it is eclipsed by such superior, newer devices.
Only real complaint I have thus far about the N3 is the tons and tons of bloatware, which wasn't ever present on the GN, and a pretty steep learning curve for simpletons such as myself.
The one real major upgrade for me personally is the signal strength. I office in a big, metal warehouse. The GN either had little or no signal strength at all in this building. It became worse after a couple of their latest OS updates. The N3 maintains a weak 4G, sometimes a strong 3G signal in this building.
Excellent device so far.