All other things being equal, due to the ratio of the rear overhang to wheelbase being exactly the same for the two, they will handle the same.
What year is your Suburban? From my own personal experience, I would see if you can find an equally as nice 2015 or newer. My 2017 Suburan with the 5.3/6A/3.08 axle tows every bit as good or better than my 2012 Yukon XL 5.3/6A/3.42. Yeah, most of the time with the 3.08 I drop it to 4th and let it run. It does less shifting than the 3.42 did running in 5th and gets better gas mileage doing it. It also get more consistent and better gas mileage not towing.
As a side note, the 2015 and newer truck have about 70 more HP and 52 more #-ft of torque than a 2003 and older truck.