YEAH ... well, if two computer connect to same internet individually (no router, no internet sharing) then you should be able to get about same internet speed, given no malware or other crap slowing down internet for some reason. this means that for same browser on both pc's, you with same configurations, you should be able to access same webpages at about same speeds.
Now, if you're lacking memory for pc, your computer will be slow and applications will load slow. That has nothing to do with internet connection speed.
But to say some browsers are slower than others, well you can tweak browsers for faster speed, you can see how much CPU % it's using.