I’m afraid the SVN Mirror add-on doesn’t provide any features that could automatically compare history in SVN and Git and neither I’m aware of any third-party tools that could do it.
There’s a couple of features that may be helpful for the history checking, I suppose. First, the add-on adds git notes during the translation; those notes contain revisions numbers. The notes can be added to the ‘git log’ output in the following ways:
in the working copy add the fetch configuration for notes in Git configuration file:
fetch = +refs/svn/map:refs/notes/commits
in the bare repository (on Bitbucket server) use the following command:
git update-ref refs/notes/commits refs/svn/map
Also, the add-on allows adding revision numbers right into commit messages during the translation. It can be done by the svn.gitCommitMessage – this setting allows to add the revision number (along with other information) in the Git commit message, which can also be useful for history comparison.