i can assure everyone there is no debate.
If you run (from a root prompt):
# adb logcat
then look carefully, you will see that even with Wifi active, the phone is accessing the LTE network for updates and transmitting data to the network, therefore using 2x the battery usage. the best way to use only Wifi is to use Airplane mode then turn on your Wifi ONLY. this assures you of a near 100% Wifi only usage.
Only then can you produce accurate results for battery usage regarding LTE vs Wifi
Current Device: SGN2 i317M - Stock & Rooted
SGSIII -SIM Unlocked/Stock ICS
SGS i9000 - CWM, XBeaned to HELL!!
Samsung Galaxy Nexus JRO03C:I9250XXLF1 - (blew it up)
SG Note i717m (sold it)
Please remember to click on THANKS! if my post here helped you in any way!!
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