So, I have heard from several places that Silver shakers are superior to Stainless Steel shakers because they cool drinks down faster. Looking up some number, Silver has a significantly higher Thermal Conductivity (429 vs 20ish W/M*K). Silver also has a specific heat about half (233 vs 500 J/Kg*K). I believe that there is a direct correlation with thermal conductivity and the heat transfer coefficient.
One argument I heard was that someone touched both the silver and the steel shakers, and the silver one felt colder. That is obvious due to the much higher thermal conductivity.
So, the point of all this, is that there are two situations, an equilibrium one, and a non-equilibrium one.
Equilibrium situation is where in the end, everything has the same temperature of 0 degrees Celsius. This will be reached much faster in the Silver case due to the higher thermal conductivity. Less heat will enter the drinks through the silver, and the less of the ice will have melted. In this case, it is obvious that Silver keeps the drink "colder" in that there is more solid ice.
Non-equilibrium would be say the stuff was allowed to sit for a certain amount of time. In that time, heat would have left the silver at a much much faster rate. In that same time, less heat has left the steel due to the much lower thermal conductivity. In this case, the Steel has left the drink cooler because the silver has put more energy into the liquid. In fact, finding something which is a great insulator, such as glass, might work even better because it transfers heat into the liquid at an even lower rate.
So, we come off with two conclusions. If we assume that most bartenders shake to the point where everything is all freezing cold, definitely true for things of exceptionally long shaking times (Ramos Gin Fizz), then obviously silver is better. What if they do only a few shakes, perhaps glass would be better?