Is there a way to let the user manage their black and white lists directly in Roundcube?
Is Roundcube the best webmail or is there something more complete?
Not by default, but one of the advantages of Roundcube is that there are many plugins available. Maybe there are plugins available that add black and white list functionality. You'll have to install and configure plugins manually, as Roundcube isn't as advanced as Wordpress for example.
The easiest method of managing black and whitelist for mailbox users is the one mentioned by @Raul A. Mailbox users can login the Plesk and (with the right permissions) can manage their own spam settings,
Roundcube focuses primarily on email. It's pretty bare bone when it comes to functionality, for example there is no calendar or any group sharing features. However the simplicity is also it's main advantage. As an more elaborate alternative you can also use SOGO webmail with Plesk.