I just finished reading the 27 pages of the Note 3 GPS Issue on the ATT Community Forums. I have an S4 Active with the EXACT SAME PROBLEMS. And, if I disabled the phone (Airplane mode) the GPS works just fine.
A bit of history - Last October I drove from New Jersey to Arkansas and back, using the "Maps" app. Worked perfectly. Also used Runtastic Pro, Endomondo Pro, and MapMyRide... NO PROBLEMS. Then, in January, 2014 I updated to Android version 4.3. Now that spring is here, I started trying to use my S4 Active on my bike rides and found the GPS was constantly dropping. I cant say I noticed it was changing from 4g to 4gLTE, but it was occurring when I was handed from one tower to the next. Repeatable at the same location.
So, it looks like we are going to have to wait until 4.4.2 comes out before we can use our expensive phone as a navigation tool. Thanks, ATT.
To summarize the 27 pages of ranting at ATT, it is not hardware, it is apparently an ATT issue, not a Samsung issue, and it seems to clear up once the Note 3 users upgraded.