If those are the only two things on your network, only having 'b' is unlikely to be a bottleneck that upgrading will fix. Is performance significantly better when you're plugged directly into the modem?

It is more a distance issue than anything else. Our apt. is about 1500 sq. feet, set up in a very linear fashion, with internal walls of brick and plaster. The wireless computer and the router are as far away as can be while still being in the same building. The speed is fine when plugged directly in, I just need a more powerful signal to reach the back of the apartment.

Maybe a different antenna?

if you have an xbox, ps3, wii, psp, cell phone, or refrigerator which uses wifi, it probably won't use N, you have to keep that in mind (I can't remember if N is b/w compatible with G).

And I'd start with the modem, for the reasons above. upgrading the modem there's a small chance that it might benefit something else you might buy. Unless you have a laptop and move around other networks, updating only your computer's card is guaranteed to not give any benefit.

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If it's distance, get one of those modems with 2/3 antennae. Or get a directional antenna for your current modem.

I've replaced the antennas on both, it helps, but not enough. Gets me from "very low" to "low."

Should I perhaps add that the router and card are, oh.... seven years old.

The real solution is to buy two new routers that both support WDS. You hook one up to your modem and put the other in the middle of your apartment to relay the signal (you don't need to run any wires to it). I can't find a decent tutorial online, but this one's kind of OK.

Get a directional antenna. 802.11B will generally go further than G, so if coverage is your problem, upgrading to 802.11G is not going to help.