First of all, there isn't a way to test your internet speed via the Xbox directly. I haven't tried this, but you may want to open Internet Explorer on your Xbox and navigate to www.speedtest.net
I haven't tried this myself so I don't know for sure if it will work.
Regarding your computer, I don't think you are seeing your true internet speed. It sounds like you are seeing the connection speed of the network interface card in your computer.
To see your real internet speed, you need to download data over a period of time and measure it. The easiest way is to use a free website such was www.speedtest.net. Try that site from your PC.
BTW, if the PC and the Xbox are on the same router/network at your home, they both are getting the same internet speed.