I agree with you guys on seeing the Predator as "badass" rather than "scary".
The very first film was more about testosterone steroid pumping action and less about horror and mystical elements. It was all macho men being beaten by an even more macho alien.
And the second film was about the same macho alien in a city filled with gun porn.
So Predator was more about the cool factor to give us an adrenaline filled experience upon seeing this badass net wearing, humanoid, crab faced, plasma shooting, spine ripping, infrared viewing, mask using, half naked, cloaking, click noise making, voice mimicking, dreadlocked ugly alien motherf**ker in action.
I think "Alien" has more of the mystical elements than Predator does personally. It's mysterious and unknown which leaves us with so many questions and speculations. Predator is straight forward "alien arrives on safari" and like with real life hunting, "safari" can be in a variety of settings whether Savannah, jungle, forest etc and in Predator's case, even suburbs.