With the same phone launching on many carriers, we sometimes get an illustration of how carriers configure things differently. Sometimes they do it for financial reasons, other times because of network compatibility. We're not sure which 'Group Messaging' falls under but evidently if you're on Verizon, you are surrendering that feature as compared to your AT&T, T-Mobile or unlocked brethren.
The Verizon HTC 8X, which gains wireless charging, appears to have lost the ability to send group messages. To clarify, this is a setting whereby the OS groups your SMS messages together for you and your friends chats. It actually uses MMS to mass deliver the messages through some network trickery and our bet is that Verizon's CDMA system for SMS is just not up to handling this features--but that's just merely a guess on our part. Regardless of the cause, the results are the same as evidenced by the above screenshot comparison: Verizon users have one less feature.
We have not verified if the Nokia Lumia 822 lack this feature too, though we assume that it does.
We suppose if big Red does figure out a way to do this they can always add it, but we're not too confident it will happen anytime soon. For more info, you can head into our forums where it is being actively discussed.