Now that we have three albums for Alice, I'll give my reasoning for Killer.
Dada's a good album, but in five times of seeing him I've yet to hear him perform a song off it. While that's not the only criteria for an "essential" album, I think it's a piece.
That leaves Killer and Billion Dollar Babies.
BDB is Alice Cooper's commercial watermark. Most fans will say Killer was the original band's creative watermark.
Each has two songs you will absolutely 100% hear him do live (BDB and No More Mr. Nice Guy off BDB and Under My Wheels and Dead Babies off Killer). Each has one song there's 50/50 chance of hearing live (Elected off BDB, which is much more likely since it's an election year, and Be My Lover off Killers).
Each has one song you'll probably hear part of as a segue to a theatrical bit (I Love the Dead off BDB and Killer off Killer).
Across the board, it's pretty much a tie for songs you'll hear live. The tiebreaker for me is the rest of each album. Both are excellent, but BDB tends to be a little "safer". Generation Landslide is about as far afield of Shock Rock as Alice gets on it. Killer, on the other hand, has two songs that really stretch what the original Alice Cooper band was. Desperado is a straight up cowboy noir song. Halo of Flies has kind of become the Holy Grail for Alice fans. At 8.5 minutes, he does it live about once a decade and when he does, boots of it get posted everywhere. Really ambitious venture into psychedelic Prog Rock.
And yes, before anyone else says it, I am just a little bit of an obsessive Alice Cooper fan...