The game is inspired by a poem. Given the inspiration, it makes sense not to break ties at all. So that's the official rule.
What do you think? Personally, I like Highest Card.
If both players have Crowns, I guess it would go to Most Crowns... then to Most 9s... and so on.
Without the tie-breaker, an Ace and 2s strategy is just as good as a Crowns and 9s strategy. So it breaks the tie according to something that isn't otherwise a strategic element in the game.
Accumulating money is already part of the game, so players should be watching it regardless of ties. Most Money as a tie-breaker seems more closely connected to the strategy of the game. (Whether or not this is decisive depends on what you want from the tie-breaker.)