If you leave out the cost of ownership, the real significant difference here is luxury. The BMW drips with it, the Cobalt skimps on it. I would honestly like to see a comparison of the performance of the two cars, because I suspect that the Cobalt may whoop on the BMW in just about every way. All that luxury comes at the cost of additional weight, and the chassis is trying to appeal to both performance and comfort, while the Cobalt has been pretty much set up with just performance in mind. The Cobalt is faster 0-60 and quarter mile, and I'd bet money that given equal drivers the Cobalt would dominate in autocross.
Of course some of you are hung up on RWD vs FWD, and are thus blind to the performance numbers. The Cobalt outperforms in pretty much every motorsports type of way (oh noes! you can't drift it!). The BMW is still impressive performance-wise, though, and has so much more luxury to it compared to the Cobalt that if you care about luxury, it's not even a comparison, but it is that way at a price.
Personally, I don't really give a crap about luxury, and refuse to own a car that's going to gouge my wallet like a BMW will, so I would without a doubt prefer the Cobalt SS.