I do believe that there should be a difference in gear acquired by PvP means or PvE means. Just because you and your team spent countless hours learning the intricacies of the Vault of Glass, doesn't mean that your gear should outclass players that leveled up using the Iron Banner and other Crucible attained gear.
This goes for the other direction.... Gear obtained from the Iron Banner should NOT outclass in PvE for players that spent the hours trying to get the Raid gear.
While I am sure some will appreciate the nice potential bump to level 30 using Iron Banner for missing gear, I do feel that this gear will more likely insult the players who fought valiantly (and by valiantly I am not meaning the cheesy way of pushing things around) to beat The Templar and Atheon to get gear that stretches their capabilities.
Weight the gear where it was acquired maybe?
IE: Gear earned from the VoG has 75% effectiveness when used against other guardians. Gear earned from Crucible has 75% effectiveness when used against agents against the Traveler.
Clutch
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Yes there should be separate gear, this way people who no life pve won't have gear advantage in a mode they don't even play...