You will find a lot of information of this everywhere on this forum.
Here's my opinions:
Stainless is expensive, aluminum is not as expensive.
Stainless very easily builds up a protective oxide layer, aluminum has to have the oxide layer created by you (boil water in it for 1 hour)
Stainless is hard to scratch and remove the oxide layer, aluminum is easier to remove the oxide layer, so don't clean with with abrasives.
Stainless is not as good as a heat conductor as aluminum, so an aluminum pot usually boils faster.
You will not get Alzheimer's from either pot, its a myth.
stainless is shiny, aluminum is not as shiny.
I use aluminum, because its cheap.
Here's what I look for in pots- Does it hold liquid? Can I boil in it? Will it break my bank account?