I'm am going to have to say the RX-7
An AWD drive launch can only do so much. Since it's a '94 and stock, it can't be pushing much more then 260hp.. but it has sequencial turbos, so very minimal turbo lag. If he has even decent tires, he'll have a very quick launch, probably not up to par with an AWD launch, but close. I've launched faster in my N/A RX-7 then my buddie's '91 TSi AWD, simply because I had 'decent' tires on and he had fairly faded tires. There is a chance you can beat him, there's a chance for anything, really. Horsepower differences aren't THAT far off, so you can win if you do it right.
My guess is that you'll be ahead, until about your first shift (even if you had a properly working second gear). I really don't see a need for the RX-7 to get into third gear.. unless you two are going all out. The only way to know for sure is to try it out. Good luck, and importantly have fun and be as safe as possible