I think that the simple answer is 'no'. Depending on what version of the DG834G you have (*), the D-Link might deliver a higher connection speed (unless your connection is a fixed speed one), so I think it would be worth trying the new router for that reason, but I don't think it will improve your wireless quality. The only reason you might want to upgrade to wireless N is to speed up transfers between the different machines on your network, if you do any of that.
* If the DG834G is a v4, then there's unlikely to be any significant difference in ADSL performance between the two routers.