Noob question on wireless routers

Sorry if this question is basic but I'm somewhat of a noob in this area. Does a dual-band wireless router make a difference on components that you have wired into it? I have an old Linksys G wireless modem with 4 ports in the back that I use to plug in my Xbox and TV. A technician came out and ran a speed test and discovered that the speed from the router was 16MB but the speed from my cable modem was 48MB. He said if I upgraded to a dual band N router then I'd see significant improvement in my Xbox bandwidth. The other option was connecting my Xbox directly into my modem but then I'd lose the wireless internet.

Did some digging on the benefits of a dual-band wireless router but doesn't this only affect wireless devices. Not sure how any wired connections that go into the router would be impacted but again I'm a noob in this area.

Thanks for the help.