I am not sure about GSM phones, but on Verizon, the bars do not indicate your data signal strength. Settings > About Phone > Status > Network Type and Strength. Lower numbers are better.
I have a year left on my Verizon contract, and I am pretty happy with them - their phone CSR's and salespeople in their corporate stores have helped me save money several times.
However, I had a landline number on AT&T available to port, so I have it on GoPhone (AT&T prepaid, no contract) to "test drive" AT&T for the next year. I bought a Moto G LTE on Amazon for $200.00 to do this.
I have unlimited data on Verizon, so I am on the $60 go phone plan which includes 2.5 GB of data, but I might drop down if my data usage isn't high after a couple of months.
The G LTE is carrier unlocked and so I can try T Mobile or a MVNO like Straight Talk later. I travel by car for work, so I am especially curious about more rural areas.
So far, data throughput speeds are higher on Verizon (more LTE-A coverage) but I am not convinced it is that different in actual use.
Posted from my XT1080M