From what I remember, the first movie showed the crew helpless not only against the alien but even against W-Y. Almost nothing is said about the Space Jockey.
The alien was depicted only in the shadows, and was revealed fully only during the latter part of the movie. That's how the idea of horror emerged: through suspense.
Because audiences already knew what the creature looked like, then they had to switch subgenres, and they chose action. But how to exemplify that given some action taking place in the first movie? Use lots of aliens.
The third movie could do neither, which is why it focused on a procedural, where the protagonists have little to wonder about the creature; they have to figure out how to use prison facilities and no weapons to kill it. (Interesting side note: one still from the first movie revealed that the crew had weapons like laser guns.)
One can say the same for the fourth movie, where different groups are involved: scientists, security, civilians, mercenaries, etc. Add to that mutations, etc.
Thus, it's all generally horror, with elements borrowed from Lovecraft, like mutations, but not much of cosmic horror, i.e., not only the origins of the aliens but the point that protagonists live in a neutral, bleak universe (note: not evil but actually neutral or uncaring).
The first point, which is depicted in more detail in the first prequel, can be entertaining if it leads to wonder, but the second is not that entertaining because it may lead to resignation, and even nihilism.
