It's a bit so-so. You should use it only if you have plenty of particle generators (both spec and console) and high aux power. Otherwise, it won't deal enough damage to be worth it, and you might as well equip something else.
It's an incredibly powerful tool in pvp, under the right circumstances, most applying to Science Vessels. For example, if an escort or BoP decides to rapid fire you, to borrow a quote from that other starry franchise, "it'll be the last mistake [they'll] ever make."
It can also be effective as a "go bother someone else for a little while" tool against cannon-shooters, particularly when they try to gank you, or even cruisers with upwards of 8 beams going at you, because that's the practical effect. They'll probably come back at you very soon after Feedback fades, but that may have bought you the time to heal back up, etc., and prevent you from getting ganked. If they do target someone for a short while instead, it probably won't be long enough to make a big difference, so I don't feel too guilty about that.
Bottom line in PVP: I'd say it's pretty darn nifty to have in a *science vessel*, though not must have, but otherwise... pick something else. It's not that it won't work on a Cruiser... but you don't want to give anyone any reasons to stop shooting you in a cruiser, and there are certainly better science powers for a cruiser in PVP scenarios, like Transfer Shield Strength and Hazard Emitters. If you're in a cruiser and you're only going to have 2-3 science powers.... Feedback isn't the one.
(And if you're using it on an escort.. you're missing the point of an escort.)
PVE, IMO it's much less useful, though not completely useless. I like it in swarm situations, like in some dailies where you have to destroy X number of sets of mobs. I'll make sure I pull at least two sets of mobs, hopefully one grouping having a trio of frigates, pop Feedback and then it does great dps. I'd use it with a cruiser or a science vessel, and it works even better if you're a science officer and can use photonic fleet (in that case, you can probably take on 3 sets of the mob groups).
(If you go the full 3 sets of mobs, the trick is you need something to keep most of the aggro on the swarm -- so your Photonic Fleet don't die, leaving you all by your lonesome -- like Tractor Repulsor Beams, esp since there's be too many mobs to realistically trap them all in a Gravity Well.)
Outside of that kind of mission, though, it's not really worth it.