For a GT automatic, you'd be surprised how well the car will perform with just tuning. Stock, a GT AT typically dyno's about 245-250 rwhp. With just tuning and 4.10 gears I was at 278 rwhp. With a bigger stall converter I'm at 283 rwhp. I've done absolutely no airflow mods (i.e. CAI, exhaust, TB, etc.), nor have I even touched the engine (i.e. cam, power adder, heads, etc.).
I've been working on driveline efficiency so that more of my car's approximately 325hp (at the crank) gets to the ground. Now I have traction problems, so drag radials are going on later this week.
So, yes, buy a hand held tuner. They all seem to work magic (SCT, DiabloSport, Hypertech, etc.).
It's likely a combination of the two. Yes, it definitely shifts harder, but you can also now roast the tires pretty well from a dead start, I imagine...that's not harder shifting, that's more power.