No. Aluminum foil has the same material properties with respect to convection and conduction of heat no matter which side faces out. The only heat that would be different would be radiated heat, which your food won't have a ton of, and even then, the dull side is still quite reflective. It's maybe one of those "technically" correct statements that the shiny side reflects more heat, but for the application of cooking, the impact is effectively zero. The retention of steam is going to be such a larger factor the side you use will effectively make no difference.

> The only heat that would be different would be radiated heat, which your food won't have a ton of

Your food won't radiate much heat, but your oven certainly does. Aluminum + broiler is like photolithography for food.

I can speak for myself: when I ask if the shiny side reflects the heat better, I don't mean to also ask if the difference is significant. It's really just curiosity, whether my school physics intuition holds up or lies to me, that's all.

So, "technically yes" is good enough answer for me.