The two different plugins are very similar in functionality, with minor differences in the user interface and in the details of the behaviour during and after the copy operation. There is no migration necessary when you migrate your instance from Server/DC to Cloud (or vice versa). You only need to install the Copy Page Tree plugin on your instance.
We strive to maintain consistency between the Server/DC and Cloud versions of the app in order to ease the transition for users moving from Server/DC to Cloud (or vice versa).
However, there are some differences that we are documenting here:
Option to copy page labels
No, they are always copied for Server/ DC
Multiple find/ replace terms
No, only SINGLE input allowed
Copy Permissions option
Yes - enabled by default
Yes - disabled by default
Remember form inputs for multiple copy operations
Progress log copy to clipboard
The Confluence server logs are easily accessible for Server/DC so this is something that may never be added to the Server/DC plugin. This was added to the Cloud plugin because the logs are not available to the user in Cloud.
The order of the inputs (the form layout) is a bit different in Server and Cloud. It would be nice to make them more consistent (by changing Server/DC). They are very similar and both are intuitive so this is a low priority.