Like any other approach in Software, each one comes with its own Pros and Cons. One could argue that an approach is chosen to serve a need/requirement.
Take an ERP system for example. Imagine a system comprised of Inventory, Accounting, Engineering processes (E.g. Maintenance Systems), Payroll, CRM etc. and all these packages belong to one complex System... Would you really want to use a single database for this? You probably could, If you want.
But the best case scenario is multiple databases. Firstly, Databases are designed(via Schemas) before they are implemented. So data integrity is not a problem at all as long as the designer knows what they're doing in terms of how the databases communicate and how they are related.
1. Performance
From performance point of view, these systems are often used by Big companies and putting such in one database bring some performance risks because that database will have to serve all of those systems at once. When each sub system in split into a distinct database, the performance will be much better because each database serves a specific sub-system(Of course since they're part of the bigger system, they do provide cross data).
2. Scalability
When it comes to scaling, It almost often doesn't matter if you're using Single or Multiple Databases. But, in our case, By splitting databases based on each subsystem, it's much easier to scale each database without affecting all the other databases. You could literally encounter a problem on the Payroll system database (down time), and not have other systems affected at the same time. Would this be the case in terms of single database? No ways!
3. Stabilization and Optimization
These really don't matter much on approach. They are mainly resource based.
4. Maintenance
Why would this be an issue if you're a big company and you can hire a lot of database admins to manage the databases specific to each sub-system? Hah aha... this really isn't a problem at all. And by knowing the schemas, there should be no difficulty in managing these databases.
Conclusion
Both approaches are better depending on when they are used. Unless you find the need to have multiple database, I would suggest that you strictly stick to a single database.