Is dovecot better than slackware's native pop3/imap server?
IMO it is. UW-imap that comes with Slackware is not actively maintained and I guess it lacks some features compared to dovecot. You can have a look here
for more details about UW-imap.
Also with postfix vs. sendmail.
Sendmail is one of the first MTAs used in linux, that's why most application that need to send out mail are calling the sendmail executable. Postfix was developed later as a (secure) alternative of sendmail and for the above reason it comes with a sendmail replacement binary.
Anyway apart from the sendmail cryptic configuration, I don't think they have any big differences. For a comparison between the most common MTAs have a look here