I can chime in on this as I own both a Chevelle and an STI.
The STI is a fantastic car when it comes to handling. Yes it has a tendency to understeer from the factory especially if you don't know how to drive it and set up your corner entry correctly but if you can get it into the corner correctly it has HUGE amounts of cornering grip and is very stable. If you do a little suspension work to them to dial out some of the understeer then they're even more fun.
With the Chevelle's longer wheelbase and quite a bit of extra weight you're already down 2 points... and the STI is a far more stable & composed chassis in hard cornering especially if there are any road irregularities involved. In corners over imperfect roads where my Chevelle will skitter sideways a little bit (especially the rear end) my STI just sticks, sticks, and sticks.
Given a "driver mismatch" (poor driver in the STI and an excellent driver in the Chevelle) you might have a chance... but the problem is the STI's chassis is so predictable and well balanced you have to be REALLY ham fisted to screw things up, to the point I'd say with an average driver in the STI compared a good driver in the Chevelle I'd probably even put money on the average STI driver. Also, the factory RE070's on the STI are darn near R-compounds from the factory. Sure they're louder than a set of Super Swampers but they are AWESOME tires in the grip department.
Also, running road race slicks on your car is probably limiting your grip on the street as I doubt you can build enough heat in them during "normal" driving to get them to really start sticking. A good example would be to try driving a car on Hoosier A-series then R-series. The A-series autocross tires start off sticky when cold but lose grip and get greasy as they get too hot, whereas the R-series roadrace versions start slicker but get sticker as heat builds in them. Different purposes for each tire-- the autocross tires start with no warmup and only have to make a 45 second or so run, whereas the roadrace tires get a couple warmup laps but then have to survive a 20 or 30 minute session. I'd venture a guess that a street/autocross oriented R-compound will yield better traction on the street than a full road race slick as you don't need to build as much heat to get the grip.
Summary:
Just wait for the turn to straighten out then pass him.