Not necessarily... not if you adjust to the proper pressure. This is the video that found the skinny to be much more compliant. Same load rating for both. But ya, if it's a choice between tires of the same dimensions, then the one with thinner and more compliant sidewalls should ride better.
I'd really like people to replicate this test with different tires... because I don't understand why they'd be so different.
I think compliance can be view very differently, how sidewall flex may not translate into ride quality, I had Yoko X-AT and Falken At3w, both 285/75r18s, I just didn't want to do BMC at the time hence the choice, I tow a lot (still do), and did all the trail stuff with them, I'd run them at 20psi when on trail:
I'd run up to 60psi when towing heavy, and normal day to day I'd run 36psi, it wasn't bad but compare to the KO2s in c-load, it was like riding on BRICKS vs cloud.
I think pizza cutters have their place, lighter vehicles and duallys, not a Tundra.