I tried to do some back of the envelope calculations on the energy input for grass vs grain finished beef a few years ago, but gave up as there are too many unmeasured variables to make a statement one way or another. The bottom line is it takes a huge amount of energy to make meat - beef requires more than pork which requires more than chicken which requires more than insects.
A piece in the Washington Post looks at some of the issues. "grass fed" only means grass finished and there is a lot of variation in how it is done. In some cases it is not as good (in some set of metrics) than grain finished.