Both logos are simple and strong if you can look past the wordmarks in the Stars logo. Unfortunately, for this point, I can't.
The all-consuming ball of fire we call a Star would have its way with anything on this planet. Even the Blues and those who sing them.
The Blues logo is a blue musical note. Very fitting. I did like the shoulder logo they wore in the '90s with the blue trumpets but I think most St. Louis fans would revolt over that one. As for the Stars, if you can go beyond the wordmarks, which I can for this point, you can't help but notice the the giant star is by itself — like the Lone Star State of Texas. The Blues logo really makes no references to the Gateway City.