Hey Stefano,
On the 1.5 site what ccomment version are you using? I hope 4.2.1 - if you do, then the update should be easy. Just copy all the comment tables to the new 3.2 website and install the latest ccomment version after that. It should pick that the previous version was 4.2.1 and it will try to make all the necessary modifications to the tables.
If on the other hand you are using other version than 4.2.1, then you'll have some manual work. You'll need to do some table changes with phpmyadmin in order for the component to work as expected.
Kind regards,
Daniel