When you have a common piece of functionality to share between two apps, do you make a library for them to share, or break out a service?
The biggest difference between publishing a library or operating a service is: who controls the pace of change.
If you publish a library for people to use, you can put out new versions, but it is up to each application’s team to incorporate that new version. Upgrades are gradual and may never fully happen.
If you operate a service, you control when upgrades happen. You put the new code in production, and poof, everyone is using it. You can upgrade multiple times per day, and you control when each is complete.
If you need certain logic to be consistent between applications, consider making a service. Control the pace of change.
(For one flipside, see: From Complicated to Complex)