I am currently using my 2005 dodge Durango to tow our 24 foot TT that weights about 4700 dw. Our Durango has plenty of power with a tow capacity of 8700 pounds but even with the weight distribution/sw...
The Silverado Crew Cab will give you about 3 feet more wheelbase length, which would help with sway. You need to know how much your trailer weighs fully loaded to determine how close you are to the towing capacity of the 1500.