Well, there will be those which (coincidentally) work, there will be those that work partially and there will be those that don't work at all. A single registration actually saves everything as a snapshot (compare it with taking a photo ). If you take that snapshot on 2 different keyboards (or take a photo in 2 different places for comparison), it is very likely that it will differ greatly. In case of the registration it wil not work or work badly.
About expansionpacks. The designer has to include all the voices, drumkits etc. to make it work flawesly on a certain KB. As soon as a pack uses the preset voices or drumkits of a specific model it depends if those presetvoices or/and drumkits are in the KB you play. Yamaha has partially solved the compatibility to store / deliver voices and drum kits in the so-called 'Legacy' folder
Not to mention getting problems how/where the files are stored.
So, in this case tweaking and adjusting is the codeword…