I don't think they viewed the Western Theatre as a lesser theatre, but that depends on what you view as the "Western Theatre." In my opinion, the Western Theatre (or Cis-Mississippi, to make it easier) is the area from Georgia, Tennessee, and Kentucky west to the Mississippi River. Now, if you're talking about the Far Western Theatre (the Trans-Mississippi), now I'd say yes, that's a "lesser" theatre. Whole bunch of generals got really exiled there. D. H. Hill rose to corps command in the Cis-Mississippi Theatre. Meanwhile, Thomas F. Drayton went from division command in South Carolina to command of cavalry fighting bandits in Texas. Just my opinion.
-Stryker