Are you running Destiny in full screen mode? For whatever reason, in a multiple monitor setup, if Destiny isn't full screen it caps the framerate even if you have framerate cap turned off.
Also, I'd check to make sure the game is using the correct graphics card, look at the video settings in-game and make sure the VRAM says 8GB available. If it's a low number then it's probably trying to use your monitor as a graphics card or something.
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Destiny was running Windowed Fullscreen but while I was trying to figure this out at some point I swapped it to Fullscreen, still at about 45 frames either way. I just checked the VRAM usage and it is currently 1242 / 8171, which makes me think that it is indeed using the correct GPU.
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1242MB of VRAM usage at 1080 res is low; even with the lowest FOV and render resolution I'm way over 2000MB.