You've already mentioned the biggest one; the director's cut has the cocoon sequence.

There are a few other moments, such as a different edit when Kane is in the egg chamber (in the director's cut the Space Jockey sequence and Kane's descent is cut differently, there is a shot where he puts his tether gun down), the alien hitting Jones' box, but mostly the director's cut has a subplot about the tensions between Ripley and Lambert that wasn't part of the 1979 theatrical version — Lambert attacks Ripley outside of the medlab for attempting to quarantine the away team on Acheron (LV-426), and later Ripley calms Lambert after Dallas' death.

I think that the theatrical version is Ridley Scott's preferred cut of the film. Both versions are included on the Blu-ray (the Blu-rays have two versions for each of the four original Alien pictures).