Civic.
Neither of them look super sporty in my opinion. The Civic's interior is georgous minus the speedometer and multistyled air vents. The Chevy's interior looks.... well, too Chevy. It looks cheap, old and plastic. On the outside, the Civic is a Civic, and not incredibly sporty. However it does look very refined and classy, where-as the Chevy's large spoiler and chrome rims look awful (I sure hope those are not the actual wheels that come on it). The basic body style of the Chevy is not that great either, it looks like a late 90's body design, not a big upgrade from the Cavalier.
Of course the Civic would benefit greatly in the sporty department by using a farther back A-pillar, longer hood, and a spoiler more similar to the 99-00 Civic Si's spoiler. But the car was designed with interior room and passengers in mind.
I'm not even going to comment on the longevity or resell value of the cars, as that is not really a choice.
The Chevy is probably faster in a straight line, being supercharged and having more displacement. The powerband is much broader. I believe a comparison has already been done between an 05 RSX-S and the Cobalt SS, and the Cobalt was slightly faster in the 0-60 and 1/4 times. And since the 05 RSX-S is comparible in engine power and weight to the Civic Si, I can only assume the same would be true in a Civic Si vs Cobalt SS performance comparison. This does not, of course, say anything about engine quality or refinement. Nor does it speak of track performance.
Edit:
Here is the RSX-S vs Cobalt SS R&T article for an idea of the performance aspect (take it with a grain of salt, no mag is unbiased or perfect). The Civic Si is rumored to be taking the place of the Acura RSX for 2007 and a 2 door TSX being introduced as Acura's entry model sports car (although I think it's a horrible idea and probably not true, we'll see). Like I said, the new Civic Si and 05 RSX-S are very comparible in performance, with the Si having a slight edge due to being lighter (although I can't say for sure since I haven't found any specs on it yet). I'm going to guess that the Si and SS are going to be very close in track times.