Through WP export-import, it doesn't seam to add the new posts, only shows what content already exists (specifically the attchments).
That surprises me, but I first export all content and then use this plugin for the imports:
https://wordpress.org/plugins/wordpress-importer/
The attachments never come along, but I deal with that separately in other ways.
Can I go this in PhPMyAdmin? in a way where I can say 'take all data, update all and add new content'.
Yes, you certainly can if your phpMyAdmin (MySQL database) user has access to both and they are together at the same phpMyAdmin screen:
And, of course, I believe you can simply download the first and then upload it into the second...but I have never done that since Synchronize can do that in a matter of seconds and will even show you before it runs what changes will be made.