I've owned both, so hear me out. I bought an '03 Mach 1 brand new. Traded it after 3 years & 30K miles for my '07 GT Coupe.
Both are great cars, but very different in character. The Mach 1 was raw muscle. You feel how fast you're going as the chassis is a bit outdated. It's a smaller, more nimble car. Faster than an S197 (stock vs stock) by a small margin. It's very engaging and feels like a rough & tumble muscle car like the good old days. The brakes & handling of the Mach 1 are much better than the newer GT's.
The S197 GT's ('05+) are much more refined. Better chassis, smoother riding, better insulated. You don't feel the speed as much, and are more comfortable in a bigger car. They are deceptive in that while they're fast, they don't really feel fast, so it's kind of a numb perception of what's happening. The stock brakes suck and the narrower 235mm width tires don't hold the road as well (especially the stock 17" Pirellis - the 18" BFG's are decent).
Of, course, start modding either car and they both are monsters (in a good way). My '07 will eat my Mach 1 up in a race now, and feels like quite the musclecar (it runs the 1/4 mile in the 12.30's @ 111+ mph), but it took mods to get it to that level of raw performance. Still more comfortable than the Mach 1 ever was, but the Mach 1 wasn't uncomfortable - just less comfortable.
The 03/04 Mach 1 is my personal favorite SN95 Mustang. Wish I could have kept it along with the '07 GT, but the newer GT's are definitely great cars, as well.
Buy either and you'll have made a great choice!