The easiest way that I've found to do this is create a new blank page, create a linked database to both databases & filter the database that has the pages that you want to move.
Then, select a handful, click duplicate, then highlight the originals of the ones you've just duplicated and drag them into the new database (I find it helps if the new database is at the top of the original). If you have the projects linked in the new database, then select the cells in the bottom database (in the copies) that you want to put in the new one, copy & paste.
This, obviously, only works if you have the same related databases in both. The dragged versions will have zero links in them, but I tend to line all my linked database properties up so that they're in the same order in the top/new database that they are in the bottom database, then I can grab a load and copy & paste. E.g. if you're linking through to projects, daily journal, gratitude journal, food log etc, if you have them in the same order in the top database (the new one) that they are in the bottom one (the old one), you can grab multiple linked database fields and just pop them into the new database.
Then go back to the bottom database and delete the 'Copy of...' ones. Do this as you're going along (so duplicate, drag & drop, copy & paste properties then delete 'Copy of...') otherwise you'll end up with loads of 'Copy of...' and some that you thought you'd moved might get lost.
Again, if you're duplicating, dragging & dropping - make sure that the 'date' property is named exactly the same in both (even if you change the name in one database just while you're moving things then change it back) otherwise dragging & dropping will create a new date field.