I think Jacob summed it up nicely.
Another thing, I think the C1 takes better mic technique. IOW, you may not be able to just slam right into it wihtout sibilence problems.
However, why just those two mics?
Although I don't particularly like it on my voice, I hear a lot of guys like the AT4033 for rap. It isn't neutral like the AT4040, which I like better in general, but it is big and round. It has a graininess to it that I could see working well with rap or metal vocals. To summ it up, it's kinda big and brash sounding.
You could certainly find a music store with the AT mics. You should try them out.
FWIW, you might be able to buy a C1 and an AT4033, especially if you find them used like Jacob's C1 (although I don't know him).