How about:-
X: game for new players where you start in your hometown, basic rules and plot.
Y: for returning players - arrive externally as previous character. Reputation for being the champion and the world is much harsher to you to suit.

Pokemon centres exist sporadically & informally and only serve to recover you if you black out (if you fuck up you go back really far, and the game would ensure that obstacles replenish themselves). You have to be fiscally conservative to buy revives, ether, potions, etc., and also less reckless in battle.

The storyline could be darker and unique, but intertwined with that of the other game so that there's an actual difference between the titles. Ideally, each game is an alternate version of the same region and the relationship between the stories creates meaning and value mutually.

Before purchasing the second game you would be expected to have an existing save file on a previous gen game, which is used to transfer Pokedex information (eradicate the tedious prospect of transferring every Pokemon box-by-box), trainer stats, items and Pokemon (maybe once the storyline is completed), and information about various accomplishments such as the battle subway that might affect NPC interactions.

Obviously pokemon would still be version exclusive, but in this instance that element is not the only thing distinguishing the games.