Does the player with the most Queens get to see the back of the cards as they pick them?
So could they choose if they wanted a Property Claim or General Store card? Or would you have the player losing a card shuffle cards and randomly give the player cards to choose from (so neither player could choose what type of cards were involved)?
Yes, the player of Queens can see the card backs. They know what card type they are picking. That is an additional benefit for this player. Also, they are allowed to know what everyone has as far as card types before picking a player to steal from.