This is a great question to ask.
For many people the answer is depends on your situation.
If you have a following whom you'd like to move the needle on a chat bot is a great way to take your business page from conversation to conversion.
If you're in the building out your following phase, you might prefer to keep personally messaging, but something to be mindful of is to keep track of repeated conversations as that would be a great basis for your future buildout.