While in practice both terms will work out to basically the same, a
"Personalvermittler" is the "man in the middle" - an agent that might work both on behalf of employers looking for potential future employees and employees looking for jobs. "Personalvermittler" will never be used for recruiting in the military.
An "Anwerber" would be the literal translation of recruiter - he works exclusively for the employer looking for potential employees. "Anwerber" originates (just like recruiter) from a military term where the recruiter exclusively recruits (enlists), well recruits.
My guess is that "Personalvermittler" would be seen as the favourite job designation by recruiters, as "Anwerber" has a slightly negative undertone of forcible enlistment from history. In addition, "Anwerber" might also be used in entirely different context for press-ganging people into criminal organisations, recruiting people into drug trafficking, or "soliciting a john".