...but I'm not sure if the wifi still drains the battery quicker even though its not searching for networks.
The free app, Llama (among others, I guess), can turn off WiFi when disconnecting from a specific WiFi network (e.g. when exiting your home). It's very easy to implement on Llama. (Select the condition "Leave WiFi Network". Then select the network name. Then select the action "WiFi Off".)
However, a better solution might be to have Llama turn WiFi on AND off whenever it determines that you are near/not-near your home-- based on which cell towers that your phone is seeing. Each cell tower broadcasts a unique ID number to the phone, so you can teach Llama to roughly identify specific, well-separated locations (e.g. home, office, church, or movie theatre) and to take certain actions based on that location. (For example, silence the volume in church or turn on/off WiFi only when at/away-from home.) Such location determination isn't as accurate as GPS, but unlike battery-gobbling GPS, the cell-tower location method consumes almost no additional power. I didn't notice any decrease in battery life after installing Llama.
However, I think that if you leave the WiFi turned on with many (not all) modern smartphones, it will consume a trivial amount of power when not in range of a known network, so I'm not sure if it's worthwhile to have Llama (et al) manage the WiFi radio like that. For most (if not all) modern smartphones, I think the WiFi radio remains largely in hibernation, waking up only periodically to sniff for a known network but otherwise remaining in hibernation. On my phones, I can't tell the difference in battery life between leaving WiFi on all the time (even when out of WiFi range most of the day) and not leaving it on. In fact (since WiFi typically uses less power than mobile data at reasonably equivalent signal strengths) I wouldn't be surprised if leaving the WiFi on all the time would actually increase battery life by more quickly switching back to WiFi when back in range of a known network-- in case I forget to manually turn on WiFi.
It's impossible for me to say because there are many variables, including the phone model and service provider (since some carriers automatically switch to their public WiFi networks for phone calls), so one experiment trumps a thousand guesses. But I would encourage the OP to do some experiments to determine if turning off WiFi actually improves battery life.
