As others have implied, if you have a very good wifi signal, it will run many times faster than 3G. Sitting next to my wifi router on my desk, my wifi is frequently 10-15 times faster than 3G. On the other hand, I've been in hotels that offer "free wifi" with my room 500+ feet from the router and the 3G speed is considerably faster. (Interestingly, that doesn't translate into the same performance factor when browsing the internet. The performance of the browser mitigates the apparent speed difference.)
You can eat up battery if your phone is searching for a wifi signal, just as you can eat up battery by incessant searching for GPS. Once your phone is connected to wifi, however, there's little penalty (battery-wise) from using it.
And as others have also implied, if your phone is not connected to power and goes to sleep, it switches to 3G and ignores a wifi signal. Awakening it will turn wifi back on if your options are set to use wifi. Since my phone is usually connected to power at my desk and I use an app to control searching for wifi networks when I'm away from home, I don't worry about it.