Moto X has 5 models with different LTE bands. Does it matter which one I get? I want to purchase an LTE phone for use with T-Mobile.  According to Wikipedia model XT1053 is what I need... however it uses LTE bands that many of the other phones don't use.


What is an LTE band?
If I purchase model XT1055 and use it on TMobile will I only use LTE band 4, and the other ones are unused?
Is there an impact on battery life if using a phone that has a different LTE band then expected by the network?
Is it correct to say that these LTE bands are hard coded into the phone and can't be changed?
LTE bands are the bands of radio spectrum that the cellular networks run on.  There are 44 defined bands and different carriers in different areas use different bands to provide service.  Wikipedia has a fairly extensive list of who uses what bands.
Yes, T-Mobile operates on band 4 (aka AWS), so any other band capability on the device would go unused.
If you don't have the same band available on the phone as on the network, you won't be able to use the network period.  It would be like trying to pick up an AM radio station on an FM-only radio.
Yes.  Band availability is determined by the hardware radio set the phone was built with.