Sure, it would have been more exciting if Verizon launched its version of the iPhone with an incremented version number and splashy new hardware capabilites -- LTE! Super-Retina display! Downward-facing camera! -- but as expected, the new beastie is essentially the same as the existing iPhone 4 model.
The primary difference is that Verizon's iPhone 4 is a CDMA unit, not GSM. This of course means that users cannot migrate their handsets between AT&T and Verizon; they have different radios and will only work on their respective network flavor. (Worthy of note, though, the Verizon agreement is non-exclusive, so a Sprint-centric CDMA iPhone is not an impossibility.)
The CDMA phone is also far more limited for international roaming, so if you plan to travel overseas with your phone please think ahead. As Steve notes, CDMA is still not capable of simultaneous voice and data, so phone calls will interrupt your data sessions; you might consider letting the calls go to your voicemail, and using a Google Voice mailbox so you can get those messages while you're surfing (although it's possible Visual Voicemail will work when a data-only session is active; we'll have to try it out and see).
Along with the different radio config comes a slightly different antenna arrangement, with another infamous air gap associated with the 'grip of death.' It's not clear yet whether this will have any bearing on the phone's connectivity, but since the working assumption is that Verizon's network > AT&T's network, dropped calls and dead spots are theoretically going to be less of a problem on Big Red than on Big Blue.
The new VZW phone also sports the ability to behave as a MiFi hotspot, giving WiFi connectivity at 3G speeds for up to five devices. Although this isn't available on AT&T's plans as an official capability, the $
10 $19.99 Cydia app MyWi for jailbroken phones already enables it, so it's reasonable to think that there's not a hardware-specific change in play; Verizon already offers the capability on several Android phones. Be aware, though, it will chew through battery like a gopher in a cabbage patch. That's another reason to be happy the VZW iPhone isn't shifting form factor at all; existing cases, battery packs and audio accessories should all continue to work unmodified. If only that were true! Laptop Mag and Slashgear both confirm that the mute switch and volume buttons have moved, meaning many (but not all) existing cases won't fit (see here). D'oh.
Developing story: stay with TUAW today for all the Verizon iPhone news.