Wifi always uses less battery because it doesn't have to reach a tower (especially compared to LTE which uses more battery than 3g). It's just going to the local router.
I agree with everyone above. WiFi definitely saves battery when connected to one source. When you leave that source, your phone is constantly searching for WiFi networks, & that's what drains your battery when you leave WiFi connected. I always have WiFi on when I get home from work & when I'm doing stuff around the house on weekends. It also saves a lot of data if you have a tiered data plan, or any plan with a data cutoff.
Yeah, I leave my WiFi on when I'm at home or my gf's place. Otherwise, I use the mobile network. Unfortunately, I don't get great internet connection in Northern Virginia from my Thunderbolt. I'm not the only one: apparently, the Thunderbolt suffers from this lack of connection because it's Verizon's first 4G phone. So it's them "testing the waters" and realizing it's not that great. I'm getting good reception now but it constantly goes in and out. I got a new SIM card from the Verizon store, hoping that it does the job. We'll see by the end of the week.
Well it seems like the network connection issue is gone. I'm having absolutely no trouble connecting, and with WiFi on for most of my day, I can now get 15-18 hours of battery life with my Thunderbolt. Definitely an accomplishment, considering I'm a moderate user.