To have wi-fi "on" all the time involves very little radiation. GSM is much more, and it keeps talking (waking up) all the time, which is what you hear if you leave a phone near a computer with a sound system, or near a TV.

wi-fi (normally) uses automatic power saving mode, which means that a) when it's idle it isn't really radiating, (and when it transmits it'll send the data in bursts btw), and b) it's using very little battery.

However, some (as in 'a few') wireless routers are unable to support power saving mode, if your AP is one of those then you'll experience serious battery drain when connected. With a normal, good wi-fi router my N800 can stay online 2-3 days (or it could, when the original battery was still fresh), but with a bad router it would drain in 2-3 hours. In both cases this would be with gmail notification running, email running (and polling), skype running and connected, rss application running.