The Stars logo breaks a cardinal rule by spelling out the entire name. They all but forfeit the point just for that. But the Predators logo is just too cool to be beaten despite being a little heavy on the detail.
A Stars is a giant, all-consuming ball of fire, and if one fell to earth, not even a Predator would survive.
Both teams were given appropriate names, the Stars being a good adaptation of North Stars for the Lonestar state. The saber-toothed tiger works for Nashville since, if you weren't aware, the fossilized bones of one was found during construction of the team's arena. So it's a tough decision. Ultimately though, the Predators logo takes this point for its slick and scary design. (I wouldn't want to come face-to-face with that animal, extinct or otherwise.)