Devs who've pitched to a publisher, what do you prioritize in your vertical slice?

I'm scoping a vertical slice demo for a new game, and have been doing some light research on how other studios go about preparing their demos. It seems like there's some variation in thought on how far you have to go, and sometimes it's game-specific.

For those of you who have scoped a slice like this for purposes of meeting with publishers, what types of systems, gameplay, and/or design elements do you prioritize before you'd consider submitting to a publisher?