With External Share for Confluence and External Share for Jira
you can decide whatever to show comments on shared page or issue:
(External Share config form)
Jira Service Desk
Things are a little bit different in Jira Service Desk.
In Jira Service Desk "View comments" is called "View public comments",
and additionally there is option to enable "View internal comments":
(External Share view comment configuration for JSD)
They are directly mapping to Jira Service Desk "Internal note" and "Reply to customer" as:
View public comments -> Reply to customer
View internal comments -> Internal note
Jira Server & Data Center
On Jira Server comments can be restricted to role or group:
(Jira Server comment section with restriction select)
In this scenario External Share for Jira on server shows only comments on External Page that are not restricted.