I have a 01 Tahoe with the 5.3 and it is a champ in my opinion.
I just got done moving in to a new house and i was able to tow everything easily, if your load is really heavy put it in tow/haul mode and it will hold you in gear a little longer and give you firmer shifts.
I had to go to the dump with the trailer and they weigh you before / after and i learned that with an empty trailor i was weighing in at ~7450 (truck and trailor) and i hardly knew the traior was back there.
When i was pulling the Camaro (full weight minus front end sheet metal) i actually had to stop on a hill to double check something and i was plesantly suprised at how easily it got going from a dead stop on a hill.
A buddy of mine pulled a rock crawler jeep with a heavy trailor attached to the back of his Silverado SS (6.0l) and he didnt have any problems but he did eventually trade up to a diesel because the MPG was horrible when towing (and he was towing alot)
I really dont think you can go wrong with a 5.3 or better
You might do some reading on which years are better, i have heard that 01+ got better heads and it feels that way when i compare my Tahoe to my parents 00 Silverado w/ 5.3... i think they may have seen an engine improvement in 04 but i am not certain.
EDIT- I just read Jeff Hansons post and that reminds me that he is 100% right, the 03s did see some neat improvements and new gadgets, the part i REALLY wish i had was that double din bose radio. If you find one with a bose sound system you can go on e-bay and pick up the factory navigation and an antenna and it is pretty much a plug and play deal!!