How useful are headhunters?

Currently trying to lateral to another shop. I'm trying to figure out whether it's beneficial to go through headhunters or avoid using their services since doing so will mean the firm I'm applying to has to pay the headhunter a placement fee (which perhaps is a drawback to my candidacy?) Do headhunters provide any value-add otherwise?

Is the best course of action to browse LinkedIn for openings and try to see if I have mutual connections at those firms? 

Thanks in advance!