Is the name of the Client the same on both Servers? If so, the Client may be getting the “latest” configuration from one Server and using it for the other. Try using Virtual sub client names to create a second client configuration for one server. There are examples elsewhere in this forum, such as this one.
You’ll want to check Separate settings for this client on both servers before setting up your virtual sub client. You will also want to disable (uncheck) Allow client-side changing of the directories to backup, Allow client-side changing of settings, and Allow clients to configure components to backup on both Servers so all settings come from the Servers instead of the Client confusing things. Now, on the larger Server, go to the Client tab and add your sub client name sub1 or something else appropriate. I recommend the main Client contain your smaller backup set - identical on both Servers - and the additional files be in the virtual sub client, which you enable for backups only on the Server with the larger storage space.
After making the changes to both Servers, go back to the Activities tab and wait a few minutes. Return to the Settings tab and your list of clients should now show Clientname* and Clientname[sub1]* which you can configure separately. Be sure the selected backup settings for the base Clientname backup are the same on both Servers.
You should only need to create and maintain the virtual sub client on the larger of the two Servers. If it somehow ends up on both Servers, disable the additional File and Image backups for the sub client on the smaller Server.
Since the main and virtual sub client settings are now separate, just as if they were separate computers, you can also schedule them at different times or intervals if needed. Enjoy!