Why does turning on 3G data make my iPhone's battery die faster?
The 3G radio requires more power. If you live in a weak 3G signal area, it may also cycle a lot between EDGE and 3G; setting up the 3G connection draws more power. Finally, you may be able to save power by setting the iPhone to Fetch New Data less often (Settings > Mail, Contacts, Calendar > Fetch New Data).
Do you get less bars with 3G on than with Edge?
If you get less than a strong 5 bars, you phone will turn up the power on the radios (which will drain the battery faster).
So it could, in part, be due to your location (distance from the nearest cell tower, buildings in the way, etc.).
Furthermore, a 3G radio uses more power to send data at the higher bandwidth.