To be honest, I think your idea of using the American Dream as a thematic approach to compare these two texts is very good. You could also think about the way in which Miller's drama is considered a domestic tragedy, which is a play that focuses on the downfall of the common man, as opposed to a higher class character as we see depicted in classical tragedies.
This would be an interesting angle to follow. You would be able to compare the way in which both Steinbeck and Miller focus on working-class or lower characters and how tragedy impacts them personally. Whether it is George and Lennie, who, as itinerant workers during the Great Depression really have so little status in the world, or whether it is Willy, whose name clearly suggests the lowly status he has in the world. both texts could be considered examples of domestic tragedies by the way they focus on their protagonists as being working class individuals who are caught up in economic processes and systems that are beyond their control and leave them crushed. Both texts of course make very harsh critical comments on materialism and the economic system in America, and those that lose out from such a system.