Muzzle down in a rack makes it easier to view the pretty part of the gun besides the oil problem previously discussed. Either way you've got to be careful moving them around in a crowded safe to prevent banging either the barrels or butts together. Six one, half dozen the other.
When handling other people's shotguns I am amazed how much oil and grease they've often applied. I guess the rationale is "if a little is good a bunch must be better". A thin, almost invisible coating is all that is needed in virtually every case. Remember, grease and oil are traps for dirt and grime to grind away on metal parts.
