There is a surprisingly clear, solid correlation between an external recruiter submitting my resume to a company and me getting a poor result on the interview.
Specifically: the same interview is generally perceived more poorly by the company if I was submitted by an external recruiter, even compared to an internal recruiter, a manager there emailing me off LinkedIn, etc.
I won't say I've never had it go well. I basically always do well if it's a strongly technical interview. But a mildly technical interview tends to swing well if no external recruiter, or poorly with an external recruiter.
I can think of a few reasons that might be. I may represent myself better when I'm direct. The company may be more cautious if there's going to be an extra price tag attached to me. The company may just have reflexive distrust of external recruiters -- wouldn't be shocking.
But to add to the problems with going through a headhunter or external recruiting company, I'd add in my own experience: I'm less likely to get the job, even with the same interview.