That's too bad that you would go to a network that has less coverage and no 4G because of a logo on a button that can be covered or removed.
As far as prices, you get what you pay for. If you want to be on the best network with the best coverage and most 4G, you'll pay a little more.
Unfortunately, wanting to be on the best network also means dealing with their BS.
I live in the DFW area and actually am getting better speeds at home on their HSDPA+ than I could get from VZW LTE. Granted I had a GNex, which blows as far as LTE signals and speeds, but still pretty nifty to still get speeds as fast as my DSL. I will say call reliability and network speeds on TMo around here off crowded towers sucks and reception at my house is a bit weak even though speeds are fine. Basically though network here in DFW is a choice between Good and great. If I travelled more I would be annoyed, but really going forward the SHAFT AT&T got related to not getting to buy out TMo will mean TMo has pretty similar coverage to AT&T going forward.
Also, my DFW area here will probably be one of the first to get TMo LTE next year and the Note 2 on TMo is ready for it.