I haven't owned dragons breath, but from what I've read, gjallarhorn is preferred. I have a maxed out gjallarhorn and I can confirm that it is wickedly powerful. Make sure your characters level is high as well. My gjallarhorn is noticeably weaker when I use my level 28 warlock instead of my level 31 hunter. I noticed this during the crota raid though, so it may be more pronounced in raids.
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Not only in raids but in general this applies: 4 lvl or lower below mob: 100% damage penalty 3 lvl below mob: ~52% damage penalty 2 lvl below mob: ~42% damage penalty 1 lvl below mob: ~32% damage penalty 0 lvl below or higher than mob: 0% damage penalty