I am going to pipe in here, cause I own a lightly modded 93 Caprice Classic w/350ci.
I have personally smoked 2 Si's with my beast, and 1 lightly modded [never lost to one

] and I dont race much, but off the line, no way that I could win, once I get moving tho, I catch up fast

The caprice gets its advantage at higher speeds, seems to be geared for much higher speeds. A caprice with a rolling start has a better chance of taking an Si.
The Auto Gearbox in the caprice lets it down, but I would say that if both are stockish and the Si driver is good with a stick then the Si will take the win. As with all races tho, it depends alot on driver skill.
So conclusion: Good chance that the Civic Si will win in a short race. If you race all out, for a longer distance, then the caprice will roast you.
A side note here: If anyone with a Si or similar ride is passing through my neck of the woods, give me a call. My V8 will hand you your ass
I still say "There is no replacement for displacement"
Best way to find out who will win is to race him. Just make sure you do it as safely as possible [its never 100% safe] , and leave money out of it.
Keep us informed, id be interested to hear what happens if you try him.