Look at this map that was posted on /r/mapporn (link). I'd have guessed it was temporal, but Montana (30% federal land) entered the union at the same time as the Dakotas (3-6% federal land), all three in 1889. I also figured it must have something to do with the line being roughly where the Rocky Mountains meet the Great Plains. Homesteaders presumably didn't claim deserts, mountains, and heavily wooded areas at the same rate the claimed fertile prairies. That said, I doubt that ~45 of California and ~85% Nevada are unarable land, or BLM land only fit for pasture. What explains that clear line?
Some of this reflects the rapidity with which the West was settled, the nature of the land itself, and the political climate during and immediately after the Civil War. Because much of the arid West cannot sustain substantial populations - particularly in the form of intensive dry farming as can be found the Midwest and East, the West tends to be more urban than other parts of the nation (defying the cliché of the rural West). This leaves large tracks of land with fewer obvious uses than elsewhere, and so the federal government becomes the default land manager.
In addition, with the rise of importance and power of the federal government as a consequence of the Civil War, it was easier for the federal government to assume management of land. States admitted before the Civil War could make a case that as semi-sovereign entities, they should have access to as much land as possible; after the Civil War the federal government was less willing to yield its control of most of the land.
Of course all these are generalizations. It would be easy to poke holes in everything I have said, so take them for what they are - history as seen when flying at 30k feet. But those are the general trends and geographic circumstances that have contributed to the differences you are observing.
