Go 2500. I had a 5.7 Tundra for 6 years. LOVED the truck and power. Towed a pop-up since new. Last year I upgraded to a 28' quad bunk. Once I loaded the trailer and truck with kids and dog, the truck was hurting for power on hills and never felt that confident at highway speeds.
This spring I picked up a Ram 2500 with the 6.7. World of a difference. With the half ton I was afraid to carry anything in the truck and traveled very light on the trailer. Now I can carry the firewood and supplies in the truck and more junk in the trailer.
I am not sure what your budget is but look for deals. I had my Laramie built with almost every option and total cost (no trade) was just under 57K. You can forego a lot of options and likely hit very close to 50K which is close to what a V8 1500 costs. My dealer even had a new leftover '15 on the lot for I think $48K well equipped!
We have a '16 ram V6 for a work truck. I can't imagine towing anything over 5K with it. Keep in mind trailers not only have the weight, but the wind area to contend with too which affects more than the weight does. Get the 2500/3500 and don't look back.
One bonus of the 2500 is the Megacab option. It is SO NICE. I can carry 4 teenagers in the back seat or fold the seats flat for the dog.
2016-06-28_09-45-24 by
RoyBelluomini, on Flickr