Let's say you choose your PlayStation account as your main account when you link your Xbox account in your The Show account.
Everything you do on either console will show up. You can play an RS game on your PS and then exit MLBTS and then open MLBTS on your Xbox and the game will be there. You buy or sell a card on your Xbox and then exit MLBTS and open it on your PS, the transaction will be there (i.e. if you bought the card, it will be in your inventory).
If you purchased deluxe editions for both consoles, you will only have access to your bonus content from your PS version. To gain access to your bonus content on your Xbox, you will need to unlink the accounts.
If you play at all (open packs, play a game, earn stubs, etc.) on your Xbox before linking the accounts, you will not have access to that progress unless your accounts are unlinked. If you do any of that AFTER you have linked accounts, then your progress will show up on your PS when you open MLBTS on it.
While accounts are linked, If you BUY stubs on your PS, you will only see those stubs on your PS. If you BUY stubs on your Xbox, you will only see those stubs on your Xbox. Any stubs you earn (while linked and regardless of which console you are playing on) will show up on both consoles.
I hope that makes it a bit clearer for you.