Just Ice no slurry is a mixture of ice and air. Air has a far worse heat transfer coefficient than water, so slurry and ice is better than ice alone from a simplistic glance at the issue point of view.
Where it gets complex is at what temp is the water? If it's near zero like the ice and added that's the best, but likely it's tap water so chilling it down will rob you of some of the thermal transfer the ice could have provided for the beer. So ratios and volume of water/air/ice/esky size /plate size etc all come into play so technically none of you could actually state with hand on heart what method is best as everyone would approach it differently with different temp water addition.
I'm sure either method you pick with require some form of TLC over the dispensing period Crusty, enjoy [emoji3]