A grade 1 out in California really isn't equal to Grade 1's other places, all the good horses are in the east and midwest when it comes to dirt/synethic.
I believe the only Grade 1 dirt route for older males run in the East so far was won by Spring At Last.
You do realize that Arl Jim said Big Booster "appears to be a better horse on dirt" ? He was a very moderate claimer on dirt!