I think Rick summarised it nicely, and i agree with each of these points:
1) pot dimensions and lid design have an effect on efficiency, pot material doesn't.
2) For boiling water there's not a shred of difference.
3) Ti pots and cups are easier to handle and drink out of because the sides and rims stay relatively cool while aluminum cookware heats evenly and fully, i.e., hot!
4) I've never dented a Ti pot and pretty much all my Al pots have acquired dents, bends and the like
I will comment on the conductivity bit to clarify why it does not matter. When the flame temperature under the pot is maybe 1,500 C and the water temperature is maybe 50 C, then whether the temperature gradient across the pot base is 0.5 C or 5 C really does not matter a hoot.
Granted, HAA is cheaper though!
PS: I still have an aluminium billy from Switzerland, made around 1950. It still works just fine. >1 mm wall thickness though!