Everyone is saying that Wi-Fi is more power-efficient than 3G on smartphones.
But, I don't think so, because two radios are turned on at the same time, the 3G radio is still active when enabling Wi-Fi
There is some reliable proof to support this?
Yes, WiFi is significantly more efficient, as the protocol is completely different. Once association with access point is established, WiFi only uses energy for actual transmission of data. On the other hand 3G remains in high-power state even after transmission is done.
source: "Energy Consumption in Mobile Phones: A Measurement Study and Implications for Network Applications" Niranjan Balasubramanian, Aruna Balasubramanian, Arun Venkataramani, Department of Computer Science, University of Massachusetts Amherst
It's also worth mentioning, that WiFi has legal limit of power output of 200mW (0.2W), while 3G devices legal power limit is 2W.
Inverse square law. Just think about the distance a 3G connection has to travel to reach a cell phone tower (hundreds of feet away) vs how far it has to travel to the nearest router (not more than 10's of feet away). All of data communication between two transmission points is in the form of EM radiation.
Note that a TCP transmission download (standard type of confirmed data reception that web browsers use) is not all reception on the part of the phone. Every data packet received must be responded to with an ACKnowledgement packet back to the tower to indicate successful reception at the phone. So even when the phone is receiving, it is still actively "sending" (acknowledgement packets).
A much higher transmission power is needed to transmit data further distances. The inverse square law says that the effect of distance on a transmission link is squared.