DDR3 certainly does offer a significant performance increase over DDR2: double the memory bandwidth and much faster speeds. However, whether you see any kind of benefit is very much determined by how powerful your other components are. Could you please post a complete list of your specs so we can check that a RAM upgrade wouldn't be bottlenecked by other components?
Realistically you wont see that big a difference. Your main issue is that you have 3GB. that means you cant be running in dual channel mode.
How are you configured ?
This is how I see it.
If you have 3 1GB strips put them to one side as spare's and get 2 x 2GB DDR3 1600 strips and put them in dual channel mode.
If you do have a 2GB DDR2 strip then check the price for a second strip the same to put with the one you have in a 2 X 2GB DDR2 set up.
I have not checked prices for a good while now but you could well find that its going to work out cheaper or not that much more expensive to go with a 2 X 2GB or even a 2 X 4GB DDR3 1600 set up.