Most will, yes. But wouldn't most skilled fighters use the weapons in different ways? Yes, using it as two weapons is an option. But what about attack moves like a thrust for example? That is a two-hand maneuver, and is at least as much a dex move as strength, probably more so.
Kinda funny, after thinking about this, I had a flashback to that old Bugs Bunny 'Robin Hood' cartoon, where Daffy Duck is practicing with his staff "Ho! Ha ha! Guard! Turn! Perry! Dodge! Spin! Thrust! (thwonnnnnngggg!!!)" Now I don't know if the Warner Bros. are skilled combatants, but even they think there's more ways to use a staff than the two options you mentioned.