Which one of these offers the best API for game development? Which library is easier to use, faster, has more documentation?
Both projects support nearly the entire DirectX libraries (though SlimDX does support a bit more in the DirectX 9 space).
SlimDX is very mature, and fully featured. Some larger scale, commercial games have been written and published using SlimDX. It also provides more of a "framework" to use, and has more feature-complete documentation.
SharpDX promises slightly better performance in certain scenarios (see benchmarks). It's generated directly from the DirectX headers, so is more of a thin DirectX wrapper.