Each one is a full game, but Conquest is regarded as the harder of the two, both for its map design and objectives, as well as the fact that there are no Scouting missions in Conquest, meaning no grinding like Birthright. You can buy both of the other paths for $20 each from within the game.
Edit: If you buy your first path digitally I think you actually get a choice on which path to follow in/after Chapter 6, but if you're playing on a cartridge the game will choose for you the first time through.
XI Wiki



