Complicated problem but just looking at materials properties:

I think there is a confusion of specific heat (the amount of energy to raise the temperature one degree of a hunk of material therefore J/C/kg) and thermal conductivity (how quickly heat moves through a material - W/m/C).

It takes a bit more energy to heat up the Al than it does the Ti - but the heat will be more evenly distributed in the Al. However, it takes much more energy to raise the water by one degree c since:
1.) There is a lot more of it -3 oz pot vs 16oz of h20
2.) the specific heat of water ~4.1/g/c -> more than 4 times more than Al.
assuming a 4oz Al pot and a 3oz ti pot with two cups of water (16oz)
Al pot: 113g Al*77C*0.9J/g/C = 7858J
Ti pot: 85g Ti * 77C *0.5J/g/C = 3272J

Water in the pot: 453g h2o*77*4.1J/g/C = 143200J

So a difference of ~3% more to heat up the Al+h20 vs the Ti+h20.
If you are measuring out your fuel within 3% you are spending too much time measuring fuel.

All in all, Al gives more even heating (fewer hotspots), Ti should technically give you a more efficient heating, but these efficiencies are so negligible that it is not even worth trying to compare, pot/stove/windscreen design plays a much more important role by far, but Ti will save you some weight, gain some strength, and loose you more dollars.