Stock those engines make 295 some horse, and 335 some ftlbs of torque, which is similar to your Vortec 5.7L. The big difference between a 6.0L, 5.7L and a 5.3L is where they make their peak torque, 5.3L likes to rev, just like the old 327s, and the 6.0Ls make their torque down low, like a 400, or a big block, while the 5.7L is a nice mix of both.
Here are some power specs:
Vortec 6.0L: 300 HP, 360 ft.lbs torque @ 4000 rpm
Vortec 5.3L: 295 HP, 335 ft.lbs. torque @ 4000 rpm
Vortec 5.7L: 255 HP, 330 ft.lbs. torque @ 2800 rpm
And yes, torque management makes a huge difference in how the truck drives. Whenever you stomp on it, it majorly retards the timing so you don't put as much strain on the transmission, or wreck your engine. Removing the torque management makes those transmissions shift a lot like the older ones, more of a quick firm shift, instead of letting off for a second, making the shift, then kicking back in.
Adding a performance tune will net you more power at the cost of running higher octane fuel, without changing anything mechanical...
You can change the cam, and put a 5.7L LS1 intake on to move the powerband even further up, and make more power, but unlike the mid 80s smoggers, there are not nearly as many cheap / easy bolt on mods to increase power on these things, they are really well built right from the factory...