There isn't a best practices doc available that lists pros and cons of using Azure Functions vs App Services.
Having said that it really depends on your REST API and your goals and objectives. I would suggest reviewing performance considerations to ensure that you won't encounter any limitations. I would also consider reviewing open issues to see what others have been running into.
If you don't see stumbling blocks, then in my opinion, I would try transitioning a resource at a time. While it's possible to create REST APIs using Azure Functions, you may discover it doesn't fit very well in your existing workflow/codebase. On the other hand, you may discover it's a perfect candidate and a easy transition. There is no wrong answer but if you happen to run into issues, feel free to post your question here on Q&A or on the Azure Function repo.