Figure out the specifications for both wireless cards and post them in here (Maker, Model, etc).
Whether a wireless card is "N" (fast) or "B" (slow) or "G" (slow) will be written directly on any materials that came with it, most likely on the front of the box. If you don't have that stuff, it can be researched online once you know the maker, model, etc from above.
You said that the router is an "N" which is good, that means it can go quite fast if a computer with an N card is connected to it but it will go quite a lot slower if it has to operate in B mode because a B card is connecting to it.
Also, there is a potential that "Mixed Mode" slows down the router. Mixed mode is when a router has to do N with computer A and B with computer B. Having to run at 2 different speeds simultaneously could detract from overall performance in a number of ways.
If you do find out you have 1 N and 1 B connecting to it, I would suggest you buy an N card for the second one and set the router to N only mode. This should increase performance considerably across the board.
Also, on a separate note...
It could be the anti-virus programs on the computers if they are different or if they are the same then one could be taxing the system a whole lot more than the other one is taxing the other system.
I don't know offhand why it would tax the better system more, but there are infinitely many variables that play into this.
Installing and uninstalling things over and over again makes computers slower in general. It could be that this happened a lot with the newer PC and not much with the older one, or the older one may have had windows reinstalled recently (undoes a lot of the damage) and the newer one hasn't.
There could be any number of causes for something like this.
I can speculate all day about what it could be, but it would be better to try to look into what I have said so far before I continue on with possibilities.