I may just have a burnt out palate, but I find the flavor of a quality rye stands out in a cocktail much more than a quality bourbon. I find the basic character of a bourbon shows up in a cocktail, but a lot of the more specific flavors don't really make it through. Whenever I find a bourbon that has some flavors that I really enjoy, but just isn't fully developed or well balanced, I set that aside for mixing. You get the base flavors, but your mixers take care of balancing the drink out.
I will use THH for a Old Fashioned or Sazerac, but I rarely feel a need to use a bourbon nicer than EWSB or OWA.