Bill likes his Samsung Galaxy Note 3, but he isn't sure the antenna is all that great. Since he's moving to a new apartment that has sketchy reception, he's looking to upgrade his phone. Leo says the first thing to consider about the "bars" reception indication is that there isn't any standard for signal strength. If he wants a serious test, he can key in the code *3001#12345#, which will give him a field test for his phone. It's very accurate. The closer to zero the better the reception is.
There are also apps in Google Play that will measure his signal strength more accurately. But even then, tests are dependent on a number of factors specific to each phone. The real test is phone call quality and dropped calls.
Getting a new phone is always a good solution to this, though.