They share very similar scenes and i dont doubt that Anerson was influenced by some of the early unused ideas from the first Alien (like the pyramid).
That however does not explain why Prometheus has literally the same scenes as AVP.
Example: The excavation, the team briefing where no one knows why they are there, Weyland being on the trip, the idea of using the Chariots of the Gods concept, the two characters (the nerd and the bully) getting lost together and bonding, Weyland dying by an Alien, the last scene where an Alien bursts out of another, etc.....
This is all too much to be a coincidance and even if these ideas where in place years before AVP, there is simply no excuse to use the EXACT same set up of a previous film.
-Foreshadowing opening set many years before events of film (AvP unrated cut only)
-Scientists discover signs designed to lure humans to a hidden place where perverse alien-ish things will happen to them
-Group of scientists/mercs for mission to undisclosed destination funded by Weyland are assembled in the cargo hold of the ship by stern Company suit, and then briefed by Weyland about what they hope to find/how it could be a historic discovery for mankind, before archaeologists comment on the power point hieroglyphs seen in different ancient cultures around the world.
-Dying Weyland founder, who has designs on immortality, accompanies the crew despite being in very bad health.
-The female protagonist talks about her fathers death.
-Giant pyramid like temple structure discovered.
-Holographic projection of the structure is seen.
-One of the mercs is challenged by the female protagonist regarding taking weapons to the site.
-Journey to the site in armoured tractor type vehicles
-Enter Giger-esque interior of structure searching with torches and find ancient language carved into walls and someone asks 'can you read this?'
-The depiction of a xenomorph on the wall.
-One of the team activates the structure - thus creating sequence of catastrophic events.
-Team gets accidentally separated, the two that don’t get along (science nerd and wannabe hard man) get cut off from main group, are attacked by face creatures and die horribly. (plus sim to the two who are cut off from the others in the sacrificial chamber are attacked by face creatures)
-Discover 7ft+ ancient aliens who wear environmental face masks and create/breed alien life forms, were once worshiped as Gods by humans
-Alien in cryogenic sleep is awakened (queen/engineer)
-Ancient aliens are hostile to humans - Weyland is killed by one
-Female protagonist tries to save the survivors, and humanity itself, from the alien threat.
-Female protagonist is only human survivor to escape destruction - which prevents spread of the alien destruction on earth (Pyramid blowing up/Prometheus crashing into the Engineer's ship)
-Main alien also survives destruction (queen/engineer) and attacks her before another alien intervenes saving the female protagonist (predator/giant face hugger)
-Female protagonist escapes environment but ultimate fate is uncertain.
-Final chest burst scene & new look xeno emerges from an ancient alien. The final shot is of the chestburster screaming into the camera.