How big is the difference between playing Destiny PvP on my laggy 50" Plasma and playing on a 24" 1080P 144hz gaming monitor?
I will give a mathematical reasoning over why it doesn't make much of a difference.
The odds are already stacked against you:
1) 30 FPS
2) Controller input lag
3) Control system itself is not 1:1 and indirect
Edit: 4) Don't forget network lag !!!
Honestly, it's not enough to make a difference, if you turn off all the post processing in your TV (basically "Game mode") then it's even less, any "perceivable" difference should be more or less be a placebo effect since HDTV response time can be as much as 30ms....which is still less than what it takes to render one frame in Destiny (as it's a 30FPS game, so each frame lasts for 33.33ms).
So at best (if you have a really really poor TV and have tons of post processing turned on) you will barely be saving one frame in a 30FPS game and in a game like Destiny it makes no difference, especially not like it would in a fighting game.