Yes, you can use both the Package Deployment Model (msdb) and the Project Deployment Model (SSISDB) in tandem with no ill-effects.
As a consultant, if I walked into a place that had both, it'd indicate that they've been using SSIS before the 2012 release and there's been no reason to upgrade existing work to a new model. In heavily regulated industries, going through the bureaucracy just to make your life easier often isn't a consideration. That or someone had a very good reason for using the legacy/msdb.
A lot of "design sins" (lack of configuration, lack of logging) in the Package Deployment Model aren't a concern with the Project Deployment Mode (logging is automatic and connection managers are easily externally configurable). The Project Deployment Model also makes parent/child design patterns more easily implemented.
From a management perspective, that's the real beauty of the SSISDB. If you want to run a package, you call the native procedures and it spins up dtexec. For packages in msdb, you are looking at either an
xp_cmdshell call or a SQL Agent job as there's no native way to run them.
Backup and recovery of an SSISDB is a touch more complex due to key management but it's documented.
Deployment of packages uses two different mechanisms (dtutil vs isdeploymentwizard/managed object model/bulk insert)
Execution uses the same executable: dtexec