In our world there are 2, (Ramadan kareem - Ramadan Mubarak), now the question is which one is right and better to say?
“Ramadan Kareem” means (generous ramadan for you), it’s new to our era, it wasn’t used in old Islam times.
Some people see it’s wrong, as Ramadan is a month, because you obviously cannot describe a month with generosity, and you can’t say it’s generous to its people as it isn’t the one who gives, but Allah SWT who gives and he is who’s very generous and merciful.
Some others think the complete opposite of the above, they think it’s the month of generosity, as Allah opens the gates of the heavens so that our Duaa’s are granted, and he doubles our ‘Good deeds’ Ten times!
And “Ramadan Mubarak” means (Blessed Ramadan), Prophet Muhammad PBUH used to say it to his people.
I think Ramadan Mubarak is better, as it indicates that there’s much more blessing upon us from Allah in that month.