[bjrnjs]

I would've thought of it this way;

Is the user bringing a cart (/user/<USER_ID>/cart/<CART_ID>)?

Is he bringing his own cart (/user/<USER_ID>/cart)?

Is the store supplying a cart for the user (/cart)?

Applying real world objects and thinking, makes more sense in my mind. The third option instinctively is the most suitable way to go (IMO).