Bands 4 and 17 require specific hardware that is only available in the c6906. So no, you cannot flash a c6906 ftf on your c6903 and expect bands 4 and 17 to work. Your friends might be getting better cell reception as compared to you but.your speeds should be pretty much same.
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Hit that thanks button, trust me it won't bite.
Sony Xperia Z1 C6906 (Debranded and Sim Unlocked) on ATT US
HTC One X
HTC Desire HD