Along with climate constraints to biome activity, as explained above, the tundra and grassland soils also vary as a result of fauna species and edaphic factors like chemical concentration, ph, minerals and topography. In the various tundra regions, there may be some hardy resident species and some migratory species.
Resident species may include ptarmigan birds, arctic hare, arctic fox, musk ox. These will be noted as having survival adaptations. Migratory species may include birds and caribou. The limited number and species of fauna in the tundra restrict the soil cycle because soil building begins with organic matter.
Edaphic factors in tundra, specifically permafrost, prevents tree growth. In warmer months the limited freeze-thaw cycle is such that strong patterns of microhabitats are developed. As a result of the edaphic factor of permafrost, no true soil is built in the tundra, resulting in a thin soil layer.
In the grassland, however, vast variety of vegetation and fauna lead to a rich soil cycle with rich carbon and nitrogen cycles, thus resulting in rich soil. The factors that form soil are time, topography (edaphic factor), vegetation and fauna, and climate.
[The links provide detailed information from Radford University and The Encyclopedia of Earth, supported by the National Council for Science and the Environment.]
Soil is thin in the tundra and rich in the grassland largely because of the very different climates of the two biomes.
In grasslands, there is a long growing season and the grass grows as tall as the precipitation will let it (as long as there is water, the grass will grow). All of that grass (when it dies) provides a lot of nutrients for the soil.
By contrast, tundra supports very little vegetation. That vegetation does not put enough back into the ground to make the ground rich in this biome.