We can, though. By isolating contributing variables and comparing them to other options, we can isolate the ecological footprint of an animal per unit of body mass or useful produce.
We know how much methane cows vs other animals produce per unit of body mass, and we know cows are very high methane producers, even by ruminant standards - and cows are the most extensively farmed ruminants, too.
The carbon that enters the animal ends up either carbon dioxide, methane, or more complex carbon structures that can eventually become one or the other (and, over a very long term, it all eventually becomes carbon dioxide). Humans, for example, lean more on the carbon dioxide side, while cows emit a lot of methane. Advanced farms even use cow manure as a fuel source, though most of methane enters the atmosphere anyway. Natural decomposition of plants in the soil by soil bacteria is, in turn, less methane-emitting than either the processes happening in the rumen, or even in the human digestive system. Add to that all the maintanence overhead of cattle feed and farm management, and the differences will exacerbate even further.
Methane is a much more potent greenhouse gas, even when corrected for it's atmospheric lifespan, and hurts environment more than carbon dioxide.
All animals have more of such footprint compared to plant-soil bacteria cycle, but cows are exceptionally bad. This is why, from an ecological standpoint, beef and dairy consumption should be reduced, of not eliminated entirely.