The difference between G & N are two things (other then speed), N can run on two difference frequencies, 2.5 & 5 Ghz, this gives an advantage when there are say wireless phones, microwaves, etc... The other advantage is the distance it can travel...
Since you only have 6 MBit/s you would not be taking advantage of the speed part... If you do not experience any problems with your G network I would personally not upgrade... Its up to your if you would like to be on the cutting edge but if your game runs full speed, no lag, I would not upgrade.
You can also look into routers such as the GameLounge ones from DLink with have GameFuel... Packet prioritization to make sure you don't have lag...
Don't upgrade if your not having any problems on the internet, waste of money.. Your G network is just fine if you don't experience any issues.