With something like a cart you want as little rolling resistance as possible. So a harder and thinner tire should go faster.
Also a larger diameter tire does not do spin as fast so you should get less slowdown from the hub or from the rotational resistance.
And yet the carts with tiny wide go-card wheels/rims kick butt over the ones using bicycle tires/rims.
My guess is the smaller wider wheels have better handling, so they don't need to slow as much for corners, but still... I would think frames using the bike wheels would win out.