here in australia the GD wrx was 1390kg and the GC was 1270. both with the same engine, drivetrain, brakes, exhaust, airbags etc.
the seats on the GD are heavier, as are the wheels. that's about all i can think of that adds weight other than the chassis. and by chassis i'm including the doors/trunk. not like you can put GC doors on a GD.
i'd say it's pretty much exactly a 100kg difference. however the GD is more aerodynamic, stiffer, can fit wider tyres and there are a hell of a lot more aftermarket products available for it.
ultimately, you'd run a widebody (more grip) and caged (stiffer) GC should you be starting a track car from absolute scratch. once they're caged the stiffness difference is virtually non existent and so the extra weight/stiffness of the stock chassis on the GD is no longer an advantage because the cage is doing that job.
however, sponsors don't like GC's because there aren't as many of them so you're actually likely to end up going faster with a GD because you'll have more money you can spend on it via your sponsors.