I know it's been a while since you have camped, but what do you think you will be taking with you when you go? Truck bed loaded up with firewood, bikes, etc? Who is the "We", you and your wife, or do you guys have kids also? Asking due to the weight of the family in the truck takes away from the available payload, which could be an issue depending on the tongue weight of the loaded trailer.
With our old trailer, tw (tongue weight) of 860lbs, cab high fiberglass topper, spray in bed liner, 4 bikes and a tool box in the bed, and the 4 of us (maybe 450lbs total), we were over the gvwr of our '10 Chevy 1500 ccsb 4x4 by about 200lbs. The weight adds up very quickly! So try to think about what you may want to take with you and determine what the rough weight will be, add the family, then you can compare the available payload listed on the yellow sticker in the drivers door jamb of the trucks you are looking at and see what is left for the trailers tw.
POWER WISE, you won't have an issue with those listed motors as long as you have the proper gearing. Remember, with the 6spd and 8spd trannies, you don't need 4.10's, just make sure you have the best available towing ratio offered for the truck you choose! I never felt I needed more power with the 5.3/6spd/3.42 combo of our '10-1500, just didn't have the needed payload. Only reason we have the 2500HD now.