Reddit mentions of Cocktail Shaker 28 oz. Weighted Stainless Steel

tl;dr: It depends on how long it takes to make a drink. In my (approximate) calculations, if it takes you longer than 26 seconds to make a drink, it's better to use the tin; otherwise, glass is better.

There are two important quantities here. Heat capacity measures the ability of a material to store heat, and has units of heat (energy) per mass per temperature change. Something with a high heat capacity can store a lot of energy per unit mass for a very small change in temperature. Thermal conductivity measures how quickly energy can dissipate out of a material, and has units of power per distance per temperature change. Something with a high thermal conductivity can dissipate a lot of heat in a short amount of time (power) through a large thickness of the material (distance) for a small temperature change. These are related, but different quantities. For example, water has a heat capacity about 20 times larger than most metals, but if you touch water at 200C and metal at 200C, you'll get burned faster by the metal because it has a much higher thermal conductivity.

Now for some calculations.

At 20C, water has a heat capacity of 4.2 J/gK, glass has 0.84 J/gK, and tin has 0.21 J/gK. Glass has a thermal conductivity of about 0.8 W/Km and tin has 67 W/Km.

I haven't ordered many mixed drinks from bars, but I'm assuming that when you're done mixing it, you pour the drink into a different glass. So the amount of time it is in the tin or glass shaker is only the amount of time required to make a drink.

For our other assumptions, let's assume that a mixed drink is about 6 fl.oz., which is 0.18L and that it has about the same density (giving it a mass of 180g) and heat capacity of water. Let's assume we're using this shaker tin, which is 294g, and this mixing glass, which is 1360g.

Let's first assume that you let the drink sit in the container indefinitely (ignoring heat flow into the container from its surroundings). Then

mdrink cwater ΔTdrink = -mcontainer ccontainer ΔTcontainer.

Plugging in values, for the tin container, the drink would increase in temperature by 1.5K, while for the glass container, the drink would increase in temperature by 12K. So if you take infinitely long to prepare your drink (in a frictionless vacuum) then using the tin is better.

However, although it would reach a higher ultimate temperature, the drink would heat up much more slowly in the glass than the tin, since glass has a much lower thermal conductivity.

To describe the time evolution of the container-drink system, I set up a series of differential equations and solved them in Mathematica. If you're curious to see exactly what I did, you can see a screenshot of the notebook here. The equations are commented in the notebook and are fairly self-evident, but it would take a lot of space to explain them in detail here.

For both cases, I assumed that the reasonable range of times to make a drink is between 0-2 minutes. I used the properties described above, and assumed that the glass container has a wall thickness of 5mm, while the tin shaker has a wall thickness of 1mm. I assumed there was no heat flow into the container in either case (which for short timescales is probably reasonable unless you're holding the container while you make the drink).

The temperature evolution of the drink-mixing glass system looks like this.

The temperature evolution of the drink-tin shaker system looks like this.

The drink remains cooler in the mixing glass until 26.5 seconds have passed, at which point it overtakes the temperature of the drink in the tin shaker.

I used to use an OXO angled measuring cup (by pure happenstance—they're the only measuring cups we own), but recently transitioned to a twist on a Boston shaker: A stainless steel shaker with a measuring mixing glass. The OXO is slightly easier to read with the angle and all, but the fact that I can measure, then shake, with the mixing glass eliminates extra steps and vessels that need cleaning.