Question : N vs G

Will a N wireless router always have a better range than a G router, or is it only that the speed is faster.

I have a G router EnGenius ECB3220 (802.11b/g)
http://www.engeniustech.com/datacom/products/details.aspx?id=170
which claims to have x3 Range. I am using it as a repeater,  but it is barely making the distance with a one bar signal. Will the Belkin N Wireless Router F5D8236-4 v3
http://catalog.belkin.com/IWCatProductPage.process?Product_Id=459569
make a difference for me? Can I use it as a repeater?

Both of them will be getting their signal from a Linksys access point - WAP54G.

Thanks

Answer : N vs G

D-Link And 24-0700 7dbi indoor antenna. Here's the link:

http://www.dlink.com/products/?pid=416

Cheers,
K.