Postdata for all post types (post, page and any custom post type) are stored in exactly the same way and is returned in exactly the same way. The WP_Post are build exactly the same each time.
The use of template tags are also not different in any way. In short, what works for normal posts must work for pages and must work for a custom post type
You must be doing something wrong because displaying post date and modified date for posts and pages is exactly the same