Technically, HTC One for each of US Mobile Carrier that we mentioned above (AT&T, Sprint, T-Mobile, Verizon, C-Spire), had the same specifications for the hardware and software of the original HTC One, except for few things. The few things that we mean are the supported network connectivity and also preloaded carriers’ applications.
These are the differences between each other Carrier in US for supported network. 3G UMTS/HSPA: Sprint uses 1900/ 2100 MHz frequency with HSPA+ that can be used up to 14.4 Mbps (DL) ; AT&T Carrier uses 850 / 1900 / 2100 MHz with HSPA+ up to 21Mbps; T-Mobile uses 850/ AWS/ 1900 /2100 with HSPA+ up to 42 Mbps; Verizon uses 1900 / 2100 MHz. 3G CDMA for Sprint and Verizon uses 800 / 1900 Mhz. 4G LTE: Verizon uses 700Mhz band 13; T-Mobile, AT&T, uses 700 MHz and AWS band; Sprint uses 1900 MHz frequency.
And if you want to know the difference on the matter of preloaded applications, you can find it just by reading each of User Manual of HTC One for each of Mobile Carriers.