In terms of handling, about equal or a bit better than my Evo. In a straight line my Evo will eat the Z06... until I mod the Z a bit.
I have laid the groundwork for some Vette mods to start with... headers, exhaust, heavy duty clutch + aluminum flywheel, two piece brake rotors, leather Recaro Pole Positions, lightweight battery, lightweight stickier tires... all of that will cut 200-250 lbs off the car and add 50+ whp if I tune it. I love lightweight cars and a sub 3000 lb Z06 would feel crazy on street and the track.
But I do want to pick up my friend's Evo 9 in a couple months too. There is something about Evos that is immensely satisfying when driving them. I'd rank them Inn my top 5 driver's cars.