I don't think it's really that clear-cut, particularly when the animal-welfare and planet-welfare arguments get intertwined:

"A number of past studies have found lower greenhouse gas emissions associated with the feedlot system. One reason is that grass-fed cows gain weight more slowly, so they produce more methane (mostly in the form of belches) over their longer lifespans...

To many grass-fed advocates, this is one of the main reasons for switching to grass-fed beef. After all, cows evolved to live this way."

https://www.npr.org/sections/thesalt/2019/08/13/746576239/is...

Would be great to see a link on this. When I search, most results suggest the impact of grass-fed cattle is no different, e.g:

https://www.sciencemag.org/news/2017/10/grass-fed-cows-won-t...