I'm not sure, I'm learning English by myself :) But I think that intense is about strength or emotions, while drastic is about radical measures

This is a great question, and something native don't usually think about. :) It seems to me that "Intense" is used more broadly and more commonly, and that"Drastic" is often used to describe extreme changes or methods. For example: - That was an intense ride. - She looked at me with an intense expression. - He made drastic changes to the report. - After the usual medication didn't work, the doctor recommended a more drastic treatment. I hope this helps!