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Interesting!

https://www.engineeringtoolbox.com/specific-heat-metals-d_15... says that aluminum has twice the specific heat capacity of cast iron, and another page on that site says that it has about four times the thermal conductivity. So if your goal is to dump as much heat into your food as fast as possible, aluminum is definitely the way to go. But if you want slower heating, iron may be better.

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This isn't a complete analysis. From the same site, cast iron has a density of 6800-7800 kg/m³, whereas aluminium is around 2700 kg/m³: https://www.engineeringtoolbox.com/metal-alloys-densities-d_....

With specific heats of 0.91 kcal/(kg⋅K) for aluminium and 0.46 kcal/(kg⋅K) for cast iron, this works out to

Aluminium: ~2500 kcal/(kg⋅m³)

Cast iron: ~3100 - 3600 kcal/(kg⋅m³)

So for a pan of the same thickness/shape, cast iron should have a heat capacity that's 25-45% higher.

When using pans, I don't particularly care if they are too thick bit I do care if they are too heavy. Aluminium pan could be lighter while having equal or greater heat capacity, if it were thick enough.

I don't know if such thick aluminium pans are available, though.

It's not just the weight that you'll care about, it's also the moment of inertia, which will help/hinder your ability to reorient the pan

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