If your old '00 era 5.3 burb did the job you will like the newer 5.3 engines.
My wife sold her '06 1500 chevy 4x4 crew cab 5.3 3.73 gears 4L60E and bought a '16 same 1500 4x4 crew cab 5.3 with 3.42 gears 6L80E.
Nite and day different in tow performance especially in the 2000-2500 rpm range. Lot more low end torque over the older 5.3 that needed lots of rpm.
She drove the 6.2 with the High Country package but decided on better mpg from the 5.3 LT.
The heaviest trailer I've pulled with both is a 10k car hauler with a 7500 tractor/fel/7' mower = 9460 lbs on the trailer axles. Now her new 5.3 won't tow like my Cummins but its light years ahead of the old '06 5.3 engine.