What Facebook does well
Facebook is great for staying in touch with your customers, showing what's happening this week, announcing a deal or a closure, and building a small community around your business. It's free, it's fast, and plenty of people are already there every day.
Where Facebook holds you back
How far your posts reach is decided by the algorithm, not by you: even your followers don't see everything. A Facebook page ranks poorly on Google when someone searches for your service. It's hard to lay out your hours, your prices and all your services clearly. And in the end, that page isn't yours.
What a website does better
A website is something you own. It shows up on Google when people search for what you offer. You present all your information the way you want, without burying it in a news feed. And it works with your Google listing to push you up in local searches.
The real answer: both together
The best of both worlds is a website as your home base and Facebook as your megaphone. Your site holds all your information and makes you findable. Facebook brings people back to it and keeps the contact going. One doesn't replace the other. But if you had to build only one first, make it the website, because it's the only one that's truly yours.