Souls explained it well. Water is flowing over the die, so effectively, your surface area is calculated by how much water passes over the surface of the die in a given amount of time... where as with a passive cooled copper block, the surface area is static, because your copper isn't flowing over the die.

So the water will get a much larger surface area, but absorbs water MUCH slower than copper... so if you use copper to get the heat away from the die, then flow water over the copper, you can make the surface of the copper as large as you want, giving the water exponentially more surface area to absorb heat from.

In any given amount of time, to get the same volume of water to transfer over the hot surface area, you will have to have the water moving VERY fast over the die to make up for the raw surface area of water flowing over copper.