As per Adobe documentation https://helpx.adobe.com/experience-manager/6-3/sites/authoring/using/page-diff.html, the user must have the Modify/Create/Delete permission on the node /content/versionhistory in order to use the page diff feature which allows for the convenient side-by-side comparison of two pages with their differences highlighted.
But when we are trying to apply Modify permissions for node /content/versionhistory, it is not getting applied even after multiple attempts.
For user admin, no issue with checkbox for Modify of /content/versionhistory
The AEM Version is AEM 188.8.131.52
Can you please suggest the solution for this issue.
I assume you are trying to apply the permissions from /useradmin. Can you try it from a private window or a different browser?
If still does not work, try adding the ACL from Crxde. Check  for more details.
 User, Group and Access Rights Administration