Crucible gear is a myth, doesn't exist.
Crucible and Faction gear is BOTH PvE and PvP gear. Learn what PvP gear would actually be.
HINT: PvP gear would contain mods and perks for PvP and have useless ones for PvE. Take a look at DC Universe Online for a great example of what I am talking about.
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Flavor and canon wise, that gear IS meant for the crucible and is intended to be more PVP stylized. Technically, you're right, there's nothing about the Crucible and faction gear that makes it any more viable in PVP. That being said, doesn't that further my point? That you don't have any reason other than preference and style to WANT that gear over Vanguard gear?