Just like which gin and which vermouth you choose makes a difference to the Negroni, the same is true to the choice of whiskey and vermouth when it comes to the Boulevardier.
The texture and mouthfeel in particular are very noticeable differences when you swap whiskey brands. If you are picking a heavy vermouth like Antica Formula or something on the bitter end of the spectrum like Punt E Mes, pick a whiskey to suit. Perhaps a Bourbon with swathes of sweet vanillin from the oak, or a cask strength offering to cut through the mix.
Similarly, a lighter fruity vermouth may suit new world whiskies instead of American Bourbon or Rye.