If you are making 350 HP with a 2.5" exhaust system, you are losing at LEAST 50 HP. I personally got about 30 HP from a full 3" exhaust on a bone stock BB DET, and I was only making about 230 HP total.
We're talking about turbos here, and turbos do not like backpressure. You will make the most HP by removing your exhaust system completely. But since we can't run around with no exhaust, the idea is to get the least restrictive exhaust possible, even for cars with small turbos. If you have a turbo, ANYTHING less than 3" is choking your system.
Now if we were talking N/A, that would be totally different. N/A motors need some backpressure to make power.
As far as noise, what you do is get all 3" straight through components, but get them as long as you possibly can. Get a 20+" long muffler, a 20+" long midpipe and whatever you can do for the cat, I'm not sure how long you can get that. But the longer the individual components are, the quieter the car will be.