* The emissions from the livestock themselves should be identical given the same number of cows and the same dietary input; CO₂ output might increase for pasture-raised cattle, given the higher physical activity, but methane output (IIRC the primary concern re: cattle and their environmental impact) shouldn't change all that much
* Non-livestock emissions (from e.g. motorized equipment) seem much easier to minimize in a traditional ranch setting - especially considering that independent ranchers once upon a time ran their ranches without motorized equipment at all, and some still do - than for a modern factory farm