My daughter and I both had an iPhone 4S on ATT. We switched to me getting the Note 3 and she got the Galaxy S4 around Jan. 2014, we also switched to Verizon BUT we have one tower in our area and it has both ATT and Verizon service on it. So this is not only a good comparison of phones, but also of reception of carrier as the cell tower near me is the same for both carriers. with ATT i got 1 sometimes 2 bars. On the Galaxy S4 the reception is the same, 1 to 2 bars. BUT on my Note 3 it stays on the 2 bars more often, so i will say the Note 3 has better reception. The very important thing here is that the ATT calls were no good, they dropped, lagged, you missed about 30-40% of the conversation depending on how you held the phone. It may be 1 or 2 bars on ATT but the calls are awful unless it was 3 bars or better, i only used it for texting holding the iPhone up in the air when i hit Send. Verizon is wayyyy better, even when i get 1 to 2 bars on my Note 3 the calls are complete, no lag, no drop, people on the other end say the call is as clear as my landline. SO, Verizon at 1 bar and ATT at 1 bar are 2 VERY different animals. They use different signals and Verizons signal goes thru buildings and trees better. I think when ATT shows reception it's really a bar or more less, i noticed this after an update on my iphone, the reception had more bars but still sucked, 3 bars on Verizon is equal to 5 bars on ATT.
This is all my experience and all my opinion. Get your phone at Best Buy. Wait for deals, with new service i got my Note 3 for $250 and the S4 was $1. yes one dollar. returns, warranties and issues are easier with Best Buy than ATT store with my iPhone. With the iPhone there was a lot of "can't help ya" at he ATT store with any issues. Ask Best Buy if they'd let you switch to the iPhone is you're not satisfied with the Note 3. They have this 30 day thing, i forgot the specifics, but i think they may have said something like that, check it out.
-The Note 3 on the Verizon network blows away iPhone on ATT.
-The Note 3 has better reception than both the iPhone and the Galaxy S4.
-Tho the 4S and S4 had 1 to 2 bars, the S4 can be used for phone calls on Verizon, the 4S on ATT can't.
-ATT signal does not go thru buildings as well as Verizon signal.
-Verizon is more stable in my area (Northeast PA).
-The Samsung products and the Android system are better than Apples. Me and my kids have had iPhone 3G, 3Gs, 4, 4S.
-You can do a lot more with Android.
-If someone is saying Apple is safer go to ESET dot com and get their security to make you feel better. I didn't because i don't put sensitive data on any phone.
-The Note 3 is clearly bigger which may help reception somehow, idk.
Good luck, i love my Note 3. My brother got one and loves it. My daughter loves her S4. They're great phones.