Your car will be faster down the track.
Once that's out the way, DRIVE THAT CAR. the RX-8 is an absolute blast to drive. Not impressive spec-wise but really fun, nice cars.
the Miatas and RX-8's are no joke real fun to drive
you ought to kill it in a straight line and on a curvy road if you can drive. They don't make much power and are only 200 lbs. lighter.
Yes yes I know everyone says they handle well, but half of that is the fact that you can mat the gas and not worry about losing traction. For poor drivers that's a huge benefit to keeping it on the line. Going around a curve is very similar to going up a hill - the stronger car can accelerate faster around a curve as long as traction holds.
I'm not saying every Mustang driver will beat every RX-8 driver around every road course. I'm saying that in the real world, the RX-8 is a fine car but the lack of power is not overcome by some nebulous handling advantage. And better tires on the Mustang than the RX-8 will trump any advantage the RX-8 might have in handling. Of course, better tires on the RX-8 will trump the power advantage on the Mustang by the same token.

+1, your car will be much faster down the track, but you will have your hands full on a road track. Actually, you will have it handed to you.
I agree, I can't count the miatas that rape stock and modified z06's on road courses around here. The miata is far, far superior to a mustang on road course, even modified.
you greatly underestimate the miata. The miata is an excellent road car, very fun to drive, and will kill a mustang/camaro/vette around the corners on the track, period.
OP,if you guys are taking it to the strip, you should have the upper hand. Make sure you have more experience at the track than he does and know your track(track prep, knowing how to cut a light, weather conditions, tire pressure,). Your stock gears are going to help you on stock tires. If you are new to racing, make a couple hot laps with "NT"-no time and single runs early, so he does not know what times you are running. Good luck, get us a video!