I am a fabricator. For a small kitchen a designer should be all you need. An experienced designer will have subs like cabinet, floor, and countertop suppliers that he or she has done business with and knows their quality and pricing. You'll save money acting as your own general contractor but then you have to deal with any issues which might occur yourself.

The design build firms are going to be more cost focused. Not your needs focus. They may have a designer but this person is not really focused on what you want and need. Most likely the designer from the deign build firm is there to ensure you make choices so the build can start and the company can move on to the next project.

I would go with someone who is there just for you.