First, let me say that Cobras are great cars.
The primary advantages a 944 would have over a Mustang are weight and weight distribution. A 944 weighs less, and it has a nearly 50/50 weight distribution front to rear. This makes the car very "neutral" in cornering, so that it neither understeers nor oversteers. I would guess that even a track prepped Cobra has a tendency to understeer.
A Cobra will always be a superior car in straight-line performance. The 944 (like all Porsches) really shines in the corners. You can carry more speed through corners (because of the factors mentioned above).
As for modding. For around $2000-$4000, you can bring a 944 Turbo up to about 350 rwhp safely. Lindsey Racing sells a $4000 kit for this that covers all the bases to safely do this.
Like any vehicle, the more horsepower you want, the more needs to be changed. How fast do you want to spend?
Depending on how much money you are willing to spend, you can bring these cars up to almost any horsepower number. There are several paths to moving beyond 350 rwhp. You could wet sleeve the block to move to a larger bore. You could buy a larger turbocharger to push more air into the engine (but watch the headgasket). You could turbocharge a 3.0 liter, 16 valve S2 block. (Powerhaus did it, producing in the neighborhood of 540 rwhp.) Of course, we are talking about spending tens of thousands of dollars at that point.
Welcome to the wonderful world of Porsche, and have fun!