It's a shame that 1500 suburbans are so limited in payload and towing ability. So many people by them thinking they are a big powerful vehicle. Then you realize that the vehicle itself eats up most of it's weight carrying capacity.
You could probably pull either of those trailers and get away with it if you are very careful and don't pack much stuff.
I would go for something lighter so you don't have to worry as much. It will be a much better towing experience.
Since you have a 5.3L engine then we should all know it's not a 2500 series. If I ever buy a Suburban, and it's tempting with a growing family, it will be a 2500.