I got a Hypertech Power Programmer III at the same time as my 2001 5.3 Silverado. It has tunes for 87 and 93 octane, and both really improve low-end throttle response. It also has options to make the shifts firmer (stock shifts were mushy and there was a lot of lag from P-R or P-D), change WOT shift points, correct tire size, and some other things. My truck seemed to stay in each gear too long, and correcting tire size fixed that. The stock setting was 30", but the actual tire measurement was about 29."
The problem is that the engine knocks like a diesel above about 4000 at wide-open throttle, tuned or not. Stock, it's better with premium fuel but still noticeable. I also notice lighter pinging at low-speed cruise, especially with A/C. Hypertech reflashed the tuner with an update for pinging, but it didn't do much. I contacted them again a few years ago to see if any newer updates were available, and they said GM had trouble with pinging on some 2000-01 trucks and the tune made it worse. They actually called that first update a "ping fix."
These days, instead of tuning it and having to either keep my foot out of it or buy higher octane fuel, I just use the tuner to firm up shifts and correct the tire size.
The short answer to your question is that a tune will make a noticeable difference in throttle response and low-end power, and you'll probably find tuners with more flexible options than the one I have.