Here was Telerik's response:
"Unfortunately at the moment the migration module does not handle automatically the persistence of any user-control specific settings of the user controls. Therefore I have logged a feature request in PITS
, which you can vote for and track.
I also want to note that by default the migration module supports migrating only Sitefinity content from 3.7 to 4.x / 5.x - custom modules, controls and other logic needs to be re-created once again, using the new API, as the new version of the CMS has a very different architecture and structure in regards to 3.7. However, there are large number of controls new functionality introduced, which might cover some of the scenarios, for which you have previously built custom user controls. For registering and creating new types of controls, you can use our tool - Sitefinity Thunder
My thought on this is best described by somebody else's comment on that PITS linked to above:
"This should have been in the migration tool all along. Lack of this functionality is a bug, if you ask me. Migration tool should MIGRATE the content, along with property values for built-in controls as well as for custom user controls. If I made even a simple user control but I placed it on 20 pages in version 3.7, I will then have to manually update all 20 instances of this user control after migrating??? It's one thing that the migration tool doesn't "migrate" the custom logic in my user controls. That's OK. But the property VALUES should be migrated.