Will beech and birch accept oil stains in similar way ? Can they be mixed in woodworking projects ?

I like the way beech stains and the fact that is relatively inexepensive. I am however having diffculties finding 1/4inch beech plywood. Birch plywood is easily available in home improvement stores. i was wandering whether I could substitute cabinet door fronts with birch and build the rest from beech.
Will beech and birch accept oil stains similar way ? The unstained wood looks similar.