What vintage 5.3L and 6L are we comparing? Both with 4 speeds?
From what I know and have heard, the 6L should be as dependable as the 5.3L all things being equal.
I towed the trailer in my signature with a 1/2 ton Suburban 5.3L/4speed/3.42 and a 3/4 ton Suburban 6L/4speed/3.73 combination. Off the line they were about the same, but at cruising speed the extra torque of the 6L and the 3.73 advantage was noticeable. I was however unable to tow in OD and still had to use drive. The 3/4 ton Suburban got worse gas mileage in all conditions. Daily driving dropped from about 15mpg to 12-13mpg.
I absolutely love the 6L/6 speed combo in our van. It tows great and my wife gets a solid 15mpg in her daily driving. This is with the 3.42 axle and from what I have seen we get about 1mpg better than the 3.73 equipped trucks.