If you're reasonably satisfied with the performance of your tired old Suburban, a newer model can only be an improvement, unless it has undisclosed issues, which is always a possibility when dealing with used vehicles.
The 5.3 has done nothing but increase in power output over the past 11 years, and in trucks from 2007 on up, has a 6-speed transmission behind it.
My 2015 5.3L, 6-speed, 3.08 axle tows my enclosed utility trailer very well. If I had this truck in 2003, I may not have ever gone looking for my dually.