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I am a third-year M&A/private equity associate at a V10 firm and have been thinking recently about making a lateral move, either to a peer firm or in-house (depending on comp package). Having attended a T14 and known classmates/biglaw colleagues who have lateraled elsewhere, I know people who have used recruiters and had positive experiences. I'm considering doing the same, but am curious (i) if particular recruiters offer significantly more value than others (i.e., does using Joe Recruiter over Bill Recruiter offer enough advantage to me such that I should take time to find someone who is highly recommended), and (ii) if there isn't substantial difference from one recruiter to the next, what are the most reputable recruiting/headhunting firms which I should think about contacting? I feel like I have a million LinkedIn requests/cold e-mails and phone calls from headhunters, and it seems tough to determine which headhunter orgs are considered legit versus those with no industry clout.

Thanks for any and all advice.