To be honest I have not used a PCI wireless card in several years so i cant personally compare the two performance wise, theoretically though there should not be much difference between the two as far as I can imagine. There are some USB antennas that are attached to a wire which allow you to move them around some to improve reception.
Is there a reason for making your computer wireless? You said your router is on the first floor and the pc is in the basement correct? The locations of each in relation to each other can make a big difference, especially since it is the basement. Copper piping especially can interfere with wireless signals as well as insulation. In my basement I can get a signal on my laptop but it is weak even though I am almost directly under the router.
As for the gaming and streaming if you are able to get a strong signal you probably wouldn't notice a large distance, but I prefer the wired connection. The strength of the signal can affect performance alot, and while in games an quick signal drop can boot you out of the game server.
It may be better, if you are looking for portability in the basement, to buy a cheap router, plug that into the wired connect and set it up as an access point. Newegg and microcenter both sell routers for $20 and under which have worked fine for me for over a year.
Bottom line, if you can get a good signal it should work fine and you probably wont notice much difference, but if you can keep the wired connection that is always preferred.