Radio signal strength is just fine. I came from a Motorola RAZR MAX HD (great battery, lousy phone) and use the Note 3 for business...
I have essentially replaced my laptop with this phone.
I get 6-7 hours of screen time, about 2-3 hours talk time.
Note: the weaker your signal is, the less battery life because the phone is always trying to connect to a better signal, and the brighter you have your screen, the less battery life... this point is very important. The screen is the biggest battery hog... combined with streaming content, BOOM.. there goes the battery.