Like said before, get some slicks and practice at the track.
Your car should work better on slicks than radials w/ the manual trans.

I'd have to agree on the top end charge comment. I wouldn't count on the hemi outrunning that cobra w/ a topend charge alone. If you can make the car hook and launch it hard, keep it on an 1/8 mile track and you'll be better off.
A lot will depend on what he has done to the cobra though.