I don't have LTE in my area but AT&T's 3G in my area runs at DSL (3.5 MB) speeds (they might call it 4G without the LTE) whereas Verizon 3G in my area is miserable.
In Boston, though, speeds are excellent with both Verizon and AT&T. I do not do a lot of bandwidth-heavy things in general on my phone and would probably be fine with AT&T 3G. I decided to generally stick with Verizon and AT&T because of their generally superior coverage. Their prices are crazy but you pay for coverage.
4 x IG Prestige MP, 70 cm, 376 grams, 386 SW, ALU Power @54, Prince Syn Gut 16 @58