Using 2 routers on same network

Let's go with 802.11g. It's 54 megabits a second so that it usually greater than most internet connections.

So adding a second router won't add any speed as WiFi, even at 802.11g is faster by many times the usual internet connection.

I think it depends on the configuration of the 2 routers and the age of all the devices. Anything you connect via Ethernet will be faster than Wi-Fi, even with a slower internet connection. If you can run cables to your Xboxes and laptops, you will notice a performance increase. Try on one of your Xboxes or laptops first and test for yourself. If you can run cables everywhere, you have no need for a 2nd router. If you have a room that you cannot run a cable to, a 2nd router as a Wi-Fi bridge can help. You can utilize modern performance on older devices via Ethernet. I just completed this setup myself and highly recommend it. I have a Netgear R7000 as my main router and a R6250 as a Wi-Fi bridge on the other side of the house. My PC and PS3 connect via Ethernet to the bridge router. The bridge router connects to the main router via AC1300 Wi-Fi. Any other Wi-Fi devices connect to the main router, the Wi-Fi gets disabled on the bridge router. If you have too many devices running at the same time, it might be better to switch off the Wi-Fi on the phones while your gaming or streaming. Quality of Service settings on the router could also help.