A few years ago I derived an equation to predict 0-60 times based on HP and weight. It is surprisingly accurate. Generally within 0.5 sec. I have the file at work, but I think I can remember the constants of the equation close enough.

I was surprised that it came out as a straight line for the best correlation. This worked reasonably well for 4 second supercars all the way through 10+ sec cars it was derived for manuals, but the comparisons should be reasonably valid.

0-60 time (in seconds) = 0.35 * Weight (in pounds) / HP + 1.5

By your account there is about 300 pounds difference in passengers.

Curb weight for LX auto: 2465
Curb Weight for LS sedan auto: 2745

So about 2600 for the Civic and about 3150 - 3200 for the Integra

0.35 * 2600 / 115 * 0.35 + 1.5 = 9.41 sec
0.35 * 3150 / 140 * 0.35 + 1.5 = 9.38 sec

Pretty much a dead heat.

Did your friend do a brake stand and launch better? that could make all the difference. At the very least, it shows that the engine and weight are close enough that they probably don't much matter, things like the transmission stall speed, launching, and gearing are probably going to have larger effects.