This is exactly how I plant my garden. I buy tomato & pepper plants from the nursery, and I direct seed everything else. Good advice to watch for pests attacking the seedlings & keeping the seeds moist, but not waterlogged.
To answer your question about seeds growing as fast & yielding as much, in my experience, seeds are better. One example: my first year I did buy a few more seedlings, one being cucumbers. After 2 weeks or so I decided I wanted more cukes, so I direct seeded a few hills. It wasn't long before the seeds caught up & passed the store bought cukes. The yield was about the same, but the development was much faster.