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It works the same way and uses the same endpoint: comment trigger, private reply, and the conversation continues in Messenger.
The differences that matter in practice:
- No public reply from the automation. On Instagram you can post a visible reply under the comment as part of the flow. On Facebook Page comments that is not exposed the same way, so plan for the private reply to do the work.
- A different handover. Messenger lets you pass thread control to the Facebook Page Inbox, so a teammate takes over in Facebook's own tools and the automation stays quiet until control comes back. Instagram has no equivalent.
- The same seven day rule for private replies, and the same 24 hour window once the thread is open.
The Page audience also behaves differently. Comments on a Page post are more often questions from people who already know you, where Instagram comments on a Reel are often from strangers. That usually means the Page flow can be shorter: answer, offer one next step, hand over.
One setting to check before you blame the automation: your Page has to allow the app to manage messages, and a Page with messaging turned off in its settings will accept the connection and then deliver nothing. It is the first thing to look at when a Page flow is silent while the Instagram one works.
The Connect Messenger article covers the Page permissions and the handover setting.