Having separate database users (with separate passwords), in addition to the root user, is good practice. This allows you to protect the data for each database, so that if the password to one database is lost, it doesn't compromise the data in the other database. And you don't have to use the root password anywhere, except when doing database maintenance.
In other words, the difference between shared login for all database users, and separate logins, is that the attacker can access less data when you use separate logins. Because even if the attacker cannot access root, they can still read the data belonging to the compromised user, and maybe do some damage. But the rest of your database is protected.
This is because the most likely way attackers will gain access to your database is either through some SQL-injection type exploit in the application, or by gaining access to your network in some way, and discovering the account credentials in configuration files.
In the first case, you only lose the data in the database with the exploit. In the second case (with an attacker in your network), they still only get access to the data in the database with the leaked configuration. An in neither case will the attacker be able to access the root account.
It comes down to the principle of least privilege.
In addition, you can have different key rotation schemes for the two accounts, both in terms of how often you change passwords, and how you distribute them. And that, I suspect, is the most practical value in having different passwords. Over time, the passwords would probably diverge anyway, or cause a lot of operational headaches.