It really depends on what you want out of a phone. Both models targets a specific consumer market that is different from each other; G900 positioned as a N-series equivalent, do-it-all multimedia device while the N82, although has similar objectives, extends its functionality to give you superior mobile imaging quality.
Both model uses different variations of the Symbian OS, G900 using UIQ touch interface while the N82 uses S60 platform. Between this two, I would have to say that S60 is pretty reliable and matured now. It has been proven many times to be ahead in terms of new developments and updates.
If you expect good pictures or like taking good pictures, N82 is no doubt the device to use. Also, if you're a internet junkie that relies much on its WIFI connection, N82 is the choice too. Although G900 also has it, N82 has a full blown Nokia Web Browser that is fast and efficient. Nothing comes close to it and it still ahead of the competition (except for iPhone's Safari browser).
However, if you like a balanced device from a slim form factor to comprehensive functionality, G900 is no doubt a smart choice especially if you like the touchscreen capabilities and the need to write scribble short notes. You can do this quickly in G900 while the N82 do not have this feature due to the lack of a touchscreen. Its not as fast as N82 but it does it pretty OK. I really like the Media Center Cross Bar UI and the multimedia capabilities.
Its a touch call but both is a good product. No matter which you choose, you'll be stuck with an excellent device which make you a smart customer no matter what.

...haha.....is that means G900 is not really strong in wifi function if compare to N82? and can the wifi run smoothly on G900? if owas got problem wif the wifi, it is useless also....