Resposta curta: O WiFi requer menos energia que o 3G.
Tanto o WiFi quanto o 3G desperdiçam energia logo após concluir uma transferência. Como o telefone usa muito mais energia do que normalmente ao transferir dados, há pouco tempo após cada transferência em que o telefone ainda está usando muita energia, mesmo que não haja mais necessidade. Isso é inevitável, mas o Wi-Fi é significativamente mais eficiente que o 3G, por isso, se você passar a mesma quantidade de tempo conectado, usando a rede da mesma maneira, sua bateria descarregará mais rapidamente com o 3G.
Observe que, se você estiver usando o telefone em que a cobertura 3G é limitada, seu dispositivo desperdiçará mais energia constantemente tentando se conectar. O mesmo vale para WiFi.
Além disso, há algo que eu li sobre o fato de que, mantendo o Wi-Fi ligado o tempo todo, você está realmente desativando o 3G, aumentando assim a vida útil da bateria. De AndroidCentral :
This tip is one that seems counter-intuitive, but you can save a lot of wear and tear on your Android phone's battery if you tell it to keep the Wifi radio turned on and connected while the phone is sleeping. Your phone needs a lot of juice to keep pinging those cell towers, and even more to transmit data to and from them. Wifi radios use much less power because of their design, and they don't have to keep searching for a better access point. It's the way cellular data communication was designed, and it's a necessary evil.
But what if you're spending all day (or all evening) in one place, connected to Wifi? If you tell your phone to shut off Wifi when idle, it bounces back to cellular data (be it 2G, 3G, or 4G) and starts sucking down the electrons again when the screen shuts off. That's no good, and easy to fix:
Open the advanced Wifi settings by pressing the menu button, then Settings, Wireless & networks, Wi-Fi settings, and tapping the menu button again. You'll have a choice to either Scan, or go Advanced -- go Advanced. Tap the Wi-Fi sleep policy entry, and you'll get a pop up dialog with the choices you see in the picture above. Choose Never.
Now even when your phone goes into standby mode, you'll stay connected to Wifi and be able to get mail and messages without turning the cell radio back on and trouncing your battery life. And for the times when you're not in an area with a Wifi connection, just shut Wifi off, either through the menu or with a handy toggle widget. Your battery will thank you for it.