The best place for an Exotic Primary is PvP, as their perks and performances seem more suited to the multiplayer. Truth, Thunderlord, Pocket Infinity and Plan C are very useful in PvP, but you'll still do just well with a Legendary or even Rare Special and Heavy. I've found that the primaries pull ahead more consistently though.
In PvE, Fatebringer or Vision of Confluence are some of the go to primaries for their elemental damage. Legendaries similar to them work well here and it allows you to use an ExoticSpecial or Heavy (or Mythoclast). If you have Gjallarhorn though, the choice is obvious.
I read a post once that said Gjallarhorn is overkill for anything other than bosses, but I don't see why that's a bad thing. An eliminate the target event shows up and you don't need to wait around for another person to help. Your strike mates quit and you just pop a synth and take down the boss yourself. Your raid group is struggling outside, so you solo the portal and take down the gatekeepers in 10 seconds.
Gjallarhorn is the best PvE weapon because it's overkill. It'd just be another rocket launcher without the Wolfpack Rounds, but those make a tremendous difference. What is it - 12-20 tracking clusters that do 240 damage each? I can never count but the DPS is insane.