Tube and shell heat exchanger effectiveness is primarily driven by prime surface (hot liquid on one side and cold directly on the opposite surface). This is the same for a counterflow chiller. So it comes down to total surface area and the rate of flow of each fluid across them. Some counterflow chillers have a convoluted inner tube to increase turbulence, but the same is true in many shell and tube designs too. To get a more exact prediction than simply surface area comparisons you need to dig out the thermal dynamics formulas.
You didn't ask about plate coolers, but they are the most compact designs due to smaller passages disrupting the boundary layers in the fluids, causing turbulence plus more surface area as well. Some designs will use inserted fins to further increase the avenues for heat transfer beyond just prime surface.