Dexron is what it calls for. Your mechanic is gonna walk to the book, look up the car, and put that fluid in the car. But pretty much as long as the fluid meets the lubricity, viscosity, and additives of the specifications designated for the car, you’re golden.
If the drivers are equal then it boils down to power to weight ratio and grip. Googled the Civic and it looks like it’s probably nearabouts 180-200hp. Assuming you also mean a 1LT and not an LT1 as the 1LT is the turbo-4 and the LT1 is the v8. The 1LT has the 275 hp that you are looking at. Google says the Camaro is about 3700 pounds, and the Civic is about 2961 pounds.
The Camaro is about 13.5 pounds per HP and the Civic is about 14.8 pounds per hp. Fewer pounds per HP usually wins in a drag race, again assuming the drivers are equal and you’re able to put the power to the pavement without wheel hopping or spinning.
If you’re looking at like autocross or anything with curves, the lower overall weight of the Civic would help it in keeping brakes cool and allowing for more aggressive driving, thus a bit quicker.
There’s really only one way to find out. Take them to a grudge night at the strip and then share the slips!