First of all, the Galaxy Reverb is only capable of 3G speeds. The radio hardware won't connect to Wimax (like the EVO or S2) or to the LTE network.
But not all is lost. The LTE rollout its part of a bigger picture called Network Vision. NV is an upgrade to the Sprint's towers infrastructure that includes better reception plus faster and more stable 3G speeds.
So, if your neighbor with the Sprint phone is getting LTE, you most likely will have 3G speeds ranging from 900 kbs to 2.2 Mbs.
This is the case down here in Puerto Rico. A month ago they upgraded the towers for LTE and we are getting an average of 1.8 Mbs (Virgin Mobile 3G) during the day.