Depends one on the phone. VZW/Sprint Galaxy S3s can use LTE data while talking on the phone.
AT&T has the one up because it will work on every one of their phones, but it isn't LTE data. Just HSPA+, because none of the radios out there can support HSPA+ voice and LTE data at the same time (yet)
There are two ways that Verizon and Sprint can do simultaneous voice&data.
1. Dual antennas. One antenna for LTE data, one for CDMA voice. The iPhone cannot do this with any current design, it would require a redesign.
2. VoLTE - Voice over LTE. This uses the data connection to transmit voice, much the same way Skype or even FaceTime do. The iPhone *COULD* do this with a software upgrade. This is entirely up to a combination of Apple and the carrier.
Note: This is semi-true on AT&T as well. AT&T LTE is data-only, but since GSM (HSPA+,) supports simultaneous voice and data, the AT&T iPhone 5 just drops the data connection from LTE to HSPA+ when you're using voice. So when you're talking, you'll get slower internet speeds, but you do get data at least.
(The older EDGE network, similar to CDMA, does not allow simultaneous voice+data, so the original "2G" iPhone can't do simultaneous on any carrier; and until T-Mobile's rollout of 3G, even the 3G-capable iPhones couldn't do it on T-Mobile.)