I strongly doubt a stock Evo (or WRX STi) could beat a Z06 Vette in any category. The Vette is simply lighter and much more aerodynamic, with more power, lower center of gravity, better suspension design (double wishbones), much bigger rubber, and better weight distribution. The only advantage of the Evo is the AWD system, which would probably only be an advantage on gravel or wet asphalt or snow. But on dry pavement I think a Z06 Vette (maybe even a standard Vette) would eat it alive. You can't really compare a purpose built sports/racing car with an econobox modified for racing.
Quick check of magazine test results: Z06 is .5 sec quicker to 60 mph, 2-3 sec quicker to 100 mph and has a 20 mph advantage in top speed.