The Google GNex is sold directly from Google and is an unlocked, penta-band, GSM phone. That means it should work on any GSM/HSPA+ carrier in the world. In the US that mean it works on AT&T, T-Mo, and most prepaid carriers, but it definitely can't work on Verizon or Sprint (because they are CDMA, not GSM). This also means that the Google GNex can't get LTE 4G, only HSPA+ "4G".
The big advantage of the Google GNex is that software updates come straight from Google with no carrier involvement. So the Google GNex will always get updates first. Another advantage of having an unlocked GSM version is that you can switch between any GSM carrier by just plugging in a new SIM card. In exchange for these benefits, you're paying the full (unsubsidized) price of $350.
If you're on Verizon and want to stay with them, then you're stuck with the Verizon GNex, which is Verizon's CDMA variant. It will work just as well, but you're locked in with Verizon and will have to wait for Verizon to approve updates.