You might have the two reversed?
I don't have hands-on experience with Exim, but every "getting started with email" document on the internet seems to recommend Postfix as easier for a beginner to install.
In fact, as an old hand (been dealing with exim configs since 2001), the very first thing I did and still do is delete the default debian hell and copy-paste a simple two-screen config which then needs only 3-4 lines tweaked.
Postfix has a high learning curve; the master.cf vs main.cf and the "chaining" of email filters (milters) is a lot more of a hurdle than exims comparatively simple configuration.
The issue is mostly that postfix is installed by default more places, so it's the default, much like sendmail was. And that setting up an MTA is quite difficult anyway.
It's basically an accident of history. But both are fine in their own right, neither is inferior to the other, just trade offs.
They are both mail-trasport daemons (basically mail relays).
dovecot is comparable to Cyrus, it's not a mail relay, it's POP/IMAP server used for accessing mail from storage.