I read some of the responses, and I think there's a difference between a daycare and an in-home preschool. I run an in-home daycare and it is correct that there can be a wide range of ages that make it difficult if not impossible to constantly give exact kind of age appropriate activity and attention that both infants and preschoolers need. For instance, it's difficult to do activities like painting, puzzles, playdoh, at an accessible table when you have toddlers who want to be in everyone's business and eat their art materials. But you can do those activities when those kids are napping. It just may not have the structure that you might want in a preschool learning environment because by design it must be more flexible to accommodate everyone.
If you're talking about a home environment that has a limited age range (from say, 2.5-5), where the main focus is preschool activities and kindergarten readiness, I think the biggest difference is the size and maybe the reliability of a center vs a home environment. You'll find more staff members in a center, so if someone is sick you won't get a call saying that school is closed. In a home environment you'll likely get more 1:1 attention and focus and smaller ratios.
I can see the benefit of both... though looking back for my two I wish I would have chosen a smaller environment that was less play based (more structured) and a little bit more academic than the one I had them in. Live and learn...