Personally, in the 1/2 tons I think that Ford edges out on Chevy. But, in the new-ish trucks they are both capable. Of course the 3/4 ton will do "better" than any 1/2 ton. But, you go to the campgrounds and they are chock full of 1/2 tons towing all kinds of trailers, even 5th wheels. My uncle has the Ecoboost Ford and he pulls a flatbed with a farm tractor on it, including implements, up Black Mountain several times a year. I don't know what the weight is but, I have no doubt that it's plenty heavy, including hitch weight.
If your TV is also your daily driver, like mine, that is a consideration as well. My Suburban is towing a 5800 (dry). My limit is 7200. I never tow with anything in the tanks. It's just the two of us and a couple of pug dogs. The 5.3 Suburban 1500 isn't ideal. But, it does OK and get us where we're going. Setting the trailer brakes, getting the WD hitch right, packing the trailer without too much stuff up front are all things I do to make it work and feel stable. We have never had sway issues, the long wheel base handles the weight good. The 5.3 pulls pretty good. It needs RPMs on long uphill pulls to be happy. That took some getting used to for me.
I came out of a motorhome that had a 454/turbo 400 and would pull it's self and my little CRV anywhere. Big, huge, difference in how the big block and the small block plus transmission puts power on the road. Point is, you would be happier all around with a heavy chassis and a big powerful engine. But, the 1/2 tons will do it. It's almost a coin toss between Ford and Chevy, in real world applications. I like Chevy but, I would buy the Ford Ecoboost with the heavy tow package.
