It depends on how serious you're about your game project and how big and complex the game is.
Full-time professional game developers are ideal for serious mobile and web-based games where you plan to make it a business and monetize your audience. They are dependable, trustworthy (if you hire the right company), consistent with code delivery, and properly aligned with your long-term vision.
Meanwhile, freelancers are best for small games that you plan to launch as a hobby, with budgets usually under $10K and a timeline of 1 to 2 months.
Freelancers won't be able to build a pro-level game that would generate serious business and a serious user base. Any successful mobile or Web game you can think of has a team of expert-level developers behind it; even the simplest ones, like the Angry Birds.