I think 10X is a good fit for freelancers, but that's what I do. I've been offered full-time jobs after contracting/freelancing; I think freelancing is a good way to bypass the recruiting/hiring/HR process if you have an "in" at the company or get placed by an agent/consultancy. Some companies can attract enough good people because of their sex appeal and signup packages (Facebook, Google, Twitter). Most companies aren't so sexy and can't afford lavish signing bonuses or offer the kinds of perks you get at Google.

If you want to use an agent or consulting firm to get interviews at multiple companies you are probably better off finding a truly talented and connected recruiter -- they do exist. Ask everyone you know, including hiring managers, for referrals to good recruiters and see which names keep coming up.

Some companies don't use recruiters or consulting firms, they do their own hiring. If you've identified one or a few companies you really want to work for the best way to get interviewed is to know someone who works there.