I've been thinking about this.
First, it isn't the mere presence of cold ice that removes heat from the system, but its actual melting. Freezing water gives up heat, melting ice absorbs heat. So also larger pieces will be preferred, as they will slowly melt away, rather than expending all their capacity to take up heat at once.
Second, this heat transfer depends on a direct interface between the melting ice and the coolant water. Without some intervention, an insulating boundary layer of fluid at an equalized temperature will quickly form, hindering further heat transfer. This is why you need to stir your wort or move your IC around, and is also the principle behind a convection oven.
Now, in your pump reservoir full of water and ice, the circulation of the water prevents the formation of this insulating layer, constantly renewing the interface between ice and water. But if you use frozen bottles (or gel packs,) the boundary layer will form INSIDE the bottle, where you can do nothing about it, and heat exchange will be rendered less effective.
So it would seem to me that the best option is probably to use ice, and find a way to put the melt water to good use.