Basil Hayden's bourbon has more rye in it's mash bill than most bourbons. This gives it a nice rye character with the corn's sweetness still present.
This is the perfect bourbon for a mint julep. At 80 proof, it does not require a long dilution like a 100 proof bourbon (though if you wait long enough with 100 proof you get to the same place). And Basil Hayden's rye character shows through nicely with the mint and syrup.