BackupBuddy is a WordPress site backup/restore/migrate tool and is not designed for partial site merging as you describe.
However, the WordPress built-in export/import tools can do this for you, including pulling over media files from one site to the other. The functionality is slightly quirky in my experience (for example, to have the media files pulled over you must do a complete export rather than just pages/posts and then edit out of the export file the things you don't want before doing the import) but does seem to do the job.
I'm not specifically aware of anything else that can do this but there may be some 3rd party plugins that offer such a capability.
Your best bet would probably be to post on the WordPress.org support forum or any of the various WordPress Q/A type forums that exist.