All good composts contains beneficial aerobic bacteria and fungi that grow from the "greens" and "browns" in the ingredients.
Leaf mold contains mostly fungi, because it is 100% decomposed leaves, all "browns", and mostly fungi, not much aerobic bacteria grew in it, to make it into leaf mold.
Animal manure based composts are usually higher in nitrites from proteins and ammonium in the manures, and aerobic bacteria in the manures, than regular leaf based composts.
However, if you have a compost made from lots of grass clippings, food scraps, or cattle feeds, it will be just as high in NPK, and aerobic bacteria and fungi and some actinomycetes, as any animal manure based compost.
Good compost teas need lots of aerobic bacteria and fungi, in order to handle all the various tasks of plant/soil fertilization, disease control, and soil conditioning and building.
The entire Kingdom of God can be totally explained as an Organic Garden (Mark 4:26)