Should I go through the State/County or use a non-profit agency?

I'm a bit confused. We are planning to begin the adoption process later in the spring in Texas, and I'm not sure of the benefit of going directly through the DFPS or an agency like DePelchin or Spaulding. Is there a different level of service? Do they all have access to the same kids (we are looking for either legal risk or straight adoption)? Any help is appreciated.