Well, according to Car & Driver these are the performance specs for each car:

Civic Si (Coupe)
0-60mph: 6.7s
5-60mph: 7.5s
Skidpad: .91g
Slalom: 68.7
Braking 60-0: 128 ft
Curb weight: 2886lbs
MPG: 23/32

GTI
0-60mph: 6.0s
5-60mph: 6.8s
Skidpad: .84g
Slalom: 66.1
Braking 60-0: 126 ft
Curb weight: 3189lbs
MPG: 25/32

I got this information from a few sources, so obvious test conditions were different. Regardless, it should give you a general sense of what to expect from each car. I would have added 1/4-mile times but I couldn't really find anything reliable.

First of all, the cars are only about 300lbs apart in weight, not 600lbs as some have claimed. Secondly, the Si 4-door weighs 3000lbs so it's only about 250lbs lighter than the GTI. That's still a decent difference in weight, but it's heavy compared to older Civics. On the other hand, it means both cars have a nice rigid chassis.

From what I've read the Civic Si is easier to drive; it's more predictable especially for a less experienced driver. The Si is very balanced so it doesn't understeer easily.

So in the end it's a driver's race. The Si is more forgiving and easier to get around a track. The GTI may be more demanding, but the power output gives the driver some leeway. So ultimately neither car has a significant advantage, but I'd give the edge to the Si. If you're comparing the Si 4-door, however, I'd say the advantage falls to the GTI.

The Civic Si does win in two areas. It costs a few thousand less than the GTI. So you're getting more for the money. It also will almost definitely be more reliable than the GTI. That's in theory, however, because I bet with dealer markups Si's cost as much as GTI's.

Either way, I'd personally go for the Civic Si. But I do admit that the GTI is a cool car in it's own right.