Depends on the bird. Mine all want covered... but... my Jefferson budgie wants only top covered. In front, only the top 1/4 or less of the cage. So he can easily check on me, make sure everything is under control if he gets alarmed. Jefferson has had night-frights, and doing a top-only cover on the cage has really helped. (At this point, i do mostly cover the sides and back of cage, & he's okay with that. A year ago, it really was top-only, only hanging down a few inches or so.)
My sun conure, on the other hand wants fully covered and pitch-black. She makes this very clear.
Only exception, IF IF the room is pitch-black and I have her in smaller sleeping cage, then IF the cage is right next to my bed (like on nightstand), only then it's okay to uncover Only the very front of cage. Basically fully covered and pitch black, but has the option to see me sleeping. This is her real preference. I think she feels like she's sleeping along with me, that way. Her actual preference would be to sleep on my shoulder all night. Obviously, that is far too dangerous to allow, so small-cage nearby, me visible, is her next-best choice. (Unfortunately, due to current temperature fluctuation issues, she has to sleep in her big cage while it's cold, as the large birdie-cages are located in the most temperature-stable spot.)