This is not an ideal way but you could create a python script that makes a FGDB each night and copies all feature class, datasets, and tables to it. Once they are in the FGDB you can copy them into other database. You could always go directly from the SDE and to SDE via the script and skip the FGDB if your system permits that. Then use windows task scheduler to automatically run the script at a certain time (ex: 2 am).
Problem with this method is that you are making a copy so you have to transfer everything not just the stuff that changed. In addition, you will need to delete the stuff at the destination before copying to prevent errors and duplication. In addition, you will have to copy every version you have if you are using versioning and they won't be linked properly in the destination.