I had a 2011 Sierra 1500 with 5.3L, tow package, and towed a 24 ft trailer in the mid 6000's and it towed decently. But, I would not have wanted to tow anything heavier.
I traded that trailer into the one in my sig, that is a 34' box, 37'(ish) total lenght. Mid 9000's GVWR. I would NEVER want to try to tow that with my Sierra 1500. I traded the Sierra in (before upgrading the trailer), to my Ram 2500 CTD, and never looked back.
With the trailer you're talking, I firmly believe you are in 3/4 ton territory. I feel very comfortable and safe with my truck/trailer combo. I used my truck as my daily driver as well, and have no issues with that.. I enjoy it every day I drive it or tow with it.
With a trailer that GVWR of 9500 lbs, you are looking at about 1300-1400 lbs of tongue weight. Add passengers and truck loaded to go camping, and you likely would be out of truck GVWR.
Donno0128 has some great points on the differences. Bottom line, the 3/4 ton is just a much more stable platform all around.
You don't have to go all the way to diesel, the gassers are also very capable. But, since you are looking at a new TV, I highly encourage/suggest you go 3/4 ton at a min.
Mike
