Firefox can be a pretty heavy browser for older computers... and heavy in general. Chrome is a better, faster alternative though they both have their advantages. Let us know more details about the wireless though, please.
Compare your upload and download speeds at speedtest.net with Internet Explorer and Firefox. I highly doubt that your connection speed is slower. Perhaps your computer is being heavily taxed by Firefox (maybe installed improperly).
Upload speeds and download speeds are related to the internet connection. So when you connection is slow, so will be your download speed. Tell us what is your link speed? Example : 144 Mbit/s
Also try to ping to google.com or daniweb.com. Firefox takes up a lot of space but it usually works per normal on laptops. USB Modem speed is generally slower than having a router and a modem together. But i doubt he will reply since he has not come back for so long.