"Still, Verizon seems to be able to consistently have the best network..."

It's been my experience that this is just marketing. Remember all of the LTE interruptions last year? Verizon is still to this day the only carrier that drops on a major interstate by the airport in my market.

I think all of the networks are good enough on the voice side of things. I think slow data is good enough across all of the networks at this point. High speed data is great where and when it's available across all of the networks at this point. So, if you've got Verizon or AT&T you're likely to perceive them as having the best network because the network works well enough. It's called marketing. If people were to jump ship and try the other guys they'd likely be just as happy and have more money in their pockets at the end of the day.