Either device you should buy unlocked. There are new versions of both phones coming out in the fall. Lte is not a big battery drain if it's consistent, but you can't disable it. Whether iPhone or lumia, buy it used
In my controlled battery tests using Edge on my L900, it actually consumed a little more power than LTE. Probably something to do with the chip being optimized for LTE. Also, of you do switch to Edge, be sure to soft reset. Otherwise you drain much more quickly. I got about the same speeds using Edge.It is possible to toggle EDGE, 3G, 4G. http://forums.windowscentral.com/os-discussion/190295.htm
I switched to EDGE and got only 0.19 Mbit/sec down and 0.20 Mbit/sec up. LTE is definitely turned off when using the Diagnostic Menu tweaks Se1fcr3ation posted.