The way Korg works is newer models are fully compatible with older models. Not necessarily the other way around. PA1000 is newer than 4X, so should be no problem playing styles. There may be some voices that are substituted, not sure.
The Songbook is another thing though. It will load the PA4X Songbook, but unless the styles are in the exact same locations you will need to "find" them and resave each Songbook entry.
I'm not much into sequences, but they should work just fine I would think.