I am not a fan of Yamaha Arrangers hence I have limited practical knowledge.
Now bear with me on this, with a Korg this is an easy process where you have the individual songs (including styles, instrument voices, Fx etx) fully set up, saved and ready to play in the Songbook. We save the Songbook to USB, then save any specific User Styles that are within the saved Songs to USB. Then the USB files are simply loaded into the new Korg Arranger. The idea with a Korg is that a user can have all their own Songs, Registrations etc saved as what Korg call SET files on a USB Memory Stick and that device can be inserted into any Korg PA and the files loaded, then the new PA will be set up exactly as the users own PA. Now the reason I am explaining the Korg system is that I would expect Yamaha to have a similar system available.
You should be able to undertake a similar process on your Yamaha by an export of your Database to the USB memory stick, this may or may not include all the Registration, Style and FX settings (your manual should explain how to do this and if it does do it). You should then be able to load the database into the SX but there may be tweaking of individual songs required due to differences within the two keyboards.
Yamaha’s software Expansion Manager may also include functions for tweaking each entry.
Korg’s Songbook Editor enables such functions to be performed and I would expect Yamaha’s to be similar.
As Ray’s suggests if you can road test an SX instore that will show you if it is possible. I rather think that there will be more to it than simply copying a batch of individual files.