It’s likely to be vastly better.

Feed efficiency is critical when doing these calculations as cows inherently need energy to survive not just produce milk. As such even if you use the same crop two different sources of protein can have wildly different levels of CO2 emissions embedded in their creation. https://en.wikipedia.org/wiki/Feed_conversion_ratio

I think it is likely more efficient. That said, cows do have the advantage that the food they consume needs little to no processing in order to produce milk. The yeast needs pretty precise processing of the incoming mash both to make sure a wild yeast strain doesn't make it's way in, and to make sure the yeast ultimately produces the right proteins.

You can't just throw in grass clippings into a vat and get whey. You can throw grass clippings into a cow to get milk (though, TBF, I dislike grassy milk).