Overall, I'm not sure it's worth it for what you would gain. You'd like driving a 6.0L LS more but the gains just might not justify the extra work in your case. Here is some info to consider.

A 5.3 LS will pull harder than the stock TBI engine and it will use less gas. The 5.3 LS would not have as much low end torque as the Vortec engine though so overall you'd have to spin it at a little higher rpm to get the same power. But, they love the rpm and it's not a big deal. You would hardly know you are doing it. Still, I'd consider it to be about even on drivability compared to the Vortec so the extra work to swap one really wouldn't be worth it unless you could do it cheaper.

A 6.0L LS beats a stock Vortec torque curve pretty much everywhere. Still, it's fairly evenly matched up to the Vortec peak torque. Then, the 6.0L pulls even harder up to it's own peak torque. However, add in the fact that LS engines love to rev so it's easy to turn them a little higher and the 6.0L will easily out-run the Vortec during normal driving. Don't believe anything about a stock Vortec having way more low end torque compared to a stock 6.0L LS because it's not true. Here are some numbers.

Vortec:
255 hp (190 kW) @ 4600 RPM
330 lb·ft (450 N·m) @ 2800 RPM
about 300 lb-ft @ 1400 RPM

first gen 6.0L
300 hp (224 kW) @ 4400 RPM
360 lb·ft (488 N·m) @ 4000 RPM
about 340 lb-ft @ 2800 rpm
about 300 lb-ft @ 1400 rpm

As another consideration, an electronic transmission is really nice if you spend the time to tune it. Fine adjusting the shift points to match your driving expectations can make a big difference in how nice you find the vehicle drives. You can pretty much get it to be in the gear you want all the time. You could also get this with the TBI by using a PCM and newer transmission.