XAMPP does not open with the words "It works" by default, but the built-in webserver that comes with Mac OS X does. You should disable the built-in webserver. How to do this, read my post here:viewtopic.php?f=29&t=33072#p164978
The files that should be copied from your Windows installation to your Mac are the files inside htdocs
If you have worked with databases on your XAMPP for Windows installation, you should export all your databases and import them on your XAMPP for Mac installation. This can be done with phpMyAdmin, which you can access via http://localhost/phpmyadmin
on a XAMPP installation. Use the export/import tabs in phpMyAdmin for importing and exporting databases. When you export a database, choose to save it to a file to avoid issues with encodings. If you have large databases, it's better to export/import databases one by one to avoid a time-out during importing.