both are good
Both cars are great. I owned a Z28 with T-tops and I appreciated having the option of taking the tops off for a little fresh air. I recently bought a Z06 because I got tired of having to re-arrange the trunk area just to store the top. Also, I didn't like the idea of having the contents of my trunk on display to the public. I don't like having that much glass in the back. If you are a very tall person (~6'6") you will require the top to be removed when you race while wearing a helmet.
I drove both the Corvette Coupe and the Z06 and they both are a blast to drive. Because the Coupe is about 100 pounds heavier than the Z06, you would need about 70 more horsepower to be as fast. This can be attained with an air filter (15), MAF (5), headers (10), exhaust (15), ported throttle body/intake/head cylinders (25). (Somebody please check my estimates.) The last item is a lot of work. The total cost would be under the 3K budget that you have, if you are willing to do most of the work. However, after making this sizable investment, it would be difficult to pass on the cost to the next owner when you decide to sell.
The shorter gears in the Z06 tranny don't really help in pure, straight line acceleration, but feel great around town and on the highway. You won't miss too much here if you're only concerned about drag racing acceleration. You could also change the rear differential to a 3.73 ratio and get similar gearing to the Z06. No recalibration is required after this mod.
The wheels on the Z06 are an inch wider all around, but they don't look as good as the current 5-spoke wheels on the coupe. BTW, I think that adding the Z06 rear brake vents to a Coupe would look slightly odd. Good luck with your decision.