I have 2 Note 3 phones and both are having signal issues and dropping calls. On average I get 2 bars if I'm lucky. Most of the time I have no service. I called Verizon and at first they seemed to act like it was a device issue. However after the network team reviewed my case I was told the area I live in has lots of hills and service can be disrupted. Um... I live in Omaha, Nebraska. It's flatter than a sidewalk. So I took the device to the Verizon store and they switched the SIM card. Still no improvement. I switched to Verizon in December for improved cellular experience. Guess I should have stayed with Sprint. At least I could receive calls and texts on the sprint network.
Check in Settings, About to see which software the phones are running.
I had a similar problem after months of good service, I finally had the kit kat or 4.4 update put on my phone and all my problems were solved.
I had to go to a Samsung rep at a Best Buy to get this done. it may void my warranty so I'm keeping quiet as no hardware was touched