Alright, so I registered here as a car enthusiast just to clear up a few misconceptions about these cars.
First and foremost since you all seem to enjoy drifting allot... Both cars are very capable of drifting, the Skyline is even easier to drift however because Atessa can be disabled turning the car into an all-time RWD vehicle. There is conversions to turn the WRX into a RWD car, but it's not as simple as unhooking a quick unclipping of a wire like in the GT-R.
Now comparing these two vehicles is difficult because the winner is all based on really what you like, drag racing, drifting, road racing or rally racing? Or are you just being a poser here and going on how the car looks?
In terms of drag racing the two cars are going to come out about the same with a driver who knows how to launch the vehicles. The STi with it's full time AWD is going to have more drive train loss up top than the GT-R is, and is probably going to pull off a 1.6-1.7 60' stock with a good launch on street tires. The GT-R however will be AWD off the line, but switch over to RWD once the car feels like the tires aren't loosing traction anywhere, pulling off probably a 1.5 to 1.6 60' with once again a competent driver. After the first 60 feet barring both got a good launch the cars should run about a mid 13 second quarter mile. Now another factor here is weight. The GT-R weighs about 300lbs more than the STi (talking about the 06 STi here) so the STi will have that going for it, as well as about 40 more HP. I'm going to have to give drag to the STi as the STi I'm going to guess would come up about .2 or so seconds quicker than the GT-R barring both have competent drivers.
Drifting the GT-R is going to win hands down. A RWD car is in all ways going to be able to drift better than an AWD car. I have experience driving both as I have a 240SX which is actually soon to be powered by an RB25DET, and have had the chance of driving a WRX on numerous occasions. Also an AWD car is going to under steer far more than RWD.
Road racing is going to be a close one again, however due to the Skylines more advanced drive train I'm going to give the win to the Skyline here, plus it's proved itself time and time again as being one hell of a handler beating out almost every car it's put up against on road races. Spare me how it handles in video games, you can say the Skyline feels like it under steers all you want lol.
Rally racing hands down goes to the STi, the car was built for this and is going to own house in rallying, the Evo however will handle better in a rally race.

.
If you're a poser basing this on looks and or sound then get out of the thread, you have no place to be around cars, nor do you have any right to discuss them.
Also to the starter of this thread, next time tell which Skyline you're talking about as there are many of them, and 3 different engines. The RB20DE/T, the RB25DE/T, and the RB26DETT which is the one I discussed in this thread being out of the Skyline GT-R34.
A better car than both of these at least for drag however would be the Mitsubishi 3000GT VR4 and the 3000GT VR4 MR which runs a ~13.2 and ~12.8 stock respectively. Both these version of the VR4 however will be beat out in most road races by the STi and GT-R.