How 'used' are you looking to go? IMO, the 5.3 w/ the 6 spd transmission will probably tow as well as the 6.0 with the 4 spd. I know they put the 6.0/4 spd combo in the 1500 'Burb for a couple years (07-08, maybe?), but I'm not sure there was ever a 6.0/6 spd combo from '09 or later, in the 1500 series, at least.
Anyway, our '10 Suburban with the 5.3/6 spd/3.42 gears tows a lot better than our '05 did with the 4 spd and 4.10 gears. Drives better in every respect, really -- performance, mpg, etc all better in the '10. The 6 spd was a big improvement.
But the little 165 cid engine parked next to the Sub in my driveway out-tows the 5.3 in every way ... imagine that!