It's not even a close race for the best HD voice service in the U.S. T-Mobile US is the clear winner because it has HD voice everywhere, and it just works.  AT&T, Sprint and Verizon all have work ahead of them.

Start with four basic questions when looking at who has the best HD voice service:  Does the carrier offer HD voice service on its 3G and 4G networks? Can the carrier seamlessly move calls between 3G and 4G networks without dropping them? Can the carrier make HD voice calls between 3G and 4G networks? Does the carrier lose significant calling features when making HD voice calls in a 4G environment (i.e., VoLTE)?

All four HD voice questions address the issues of availability and functionality that we have come to expect from mobile calling without getting into pretty marketing terms, damned lies, and network coverage maps. 

T-Mobile US is currently the only cellular service provider that offers HD voice on both its 3G and 4G networks.  It launched HD voice service nationwide on its 3G network in January 2013. Voice over LTE (VoLTE) 4G service started in May, and announced nationwide coverage by the end of July.  

Sprint has nationwide HD voice coverage on its 3G CDMA network, but has no immediate plans to offer VoLTE from all accounts.  AT&T has chosen to offer HD voice via VoLTE and that's it, with company officials saying they can't/won't offer HD voice on their 3G HSPA network due to bandwidth considerations.  AT&T's deployment is roughed out to a half dozen or markets as of this moment while Verizon offers VoLTE nationwide, with no plans to offer HD voice on its 3G network.

Voice call continuity (VCC) has been a big talking point among carriers, specifically the ability to make a call on one network (3G or 4G) and to seamlessly keep a call going even if the mobile device moves out of range of one network and has to transfer over to another network.   T-Mobile boasts it is the first U.S. carrier to implement enhanced Single Radio Voice Call Continuity (eSRVCC) on its network, so calls don't get dropped if you move in or out of LTE coverage.  A spokesperson for T-Mobile says that a call made in HD voice remains in HD voice, regardless of network, and HD voice calls go through between 3G and 4G networks rather than kicked back to narrowband.

AT&T officials have discussed implementing the toolkit of LTE-Advanced and eSRVCC to seamlessly move calls between 3G and 4G networks, but since AT&T doesn't run HD voice on its 3G network, any transferred call will get kicked back to narrowband—Can't wait to hear people complain about the difference of voice quality dropping in mid-call.

Verizon's "Advanced Calling 1.0" FAQ makes no bones about it—if you start a call in VoLTE and move to a 3G network, it will drop.  The carrier is kind enough to suggest that if this is a big problem, you can turn off VoLTE calling on your handset.

Finally, Verizon appears to be the only carrier that loses caller ID information in its first release of VoLTE, specifically caller name and company name.  Advanced Calling 1.0 does not provide those bits at the moment, making it an interesting question as to what you call it when Verzion figures out how to do the same thing on VoLTE as narrowband and the other VoLTE-offering carriers.  Advanced Calling 1.0.1, perhaps?

T-Mobile US is the only carrier that, according to all answers and public information available today, can offer seamless HD voice calling on and between its HD voice networks, and does so without dropping calls or losing HD voice quality when moving between networks.  You can't make that argument for any other U.S. carrier.