Of any recycled product anywhere, aluminium recycling is far the greenest. Forty recycled cans save three litres of petrol. It uses less water and energy than all other recycling efforts, and less water and energy than aluminium mining, which is why aluminium companies are desperate for people to recycle aluminium. Recycling aluminium cans is nearly at the level of reuse, which is the greenest possible option.
Coca-Cola has experimented with aluminium bottles to replace some of its bottle plastic as oil before oil dropped relative to aluminium. Plastic is extremely difficult to recycle, and the entirety of the bottle is never recycled – there are always waste products.
Almost all plastic in consumer products comes from oil. And all plastic used for packaging comes from oil. More than 40% of the oil consumed in the US is not fuel or burned, but rather is used for chemicals, the vast majority of which are plastics. To recycle plastic, you need organic solvents (organic chemicals, not organic food). Guess where the solvents come from. That's right, oil. In addition to solvents, you also need heat, and heat comes from burning oil (mostly).
Another way to think of this is: every aluminium atom on the earth is still on the earth, either as a metal or as part of a compound. We don't really use up aluminium. If we all threw them away into a landfill we could potentially mine landfills for aluminium. Paper is basically cellulose. And some insects that will happily chomp on paper. The only problem with paper is the oil-based inks, bleaches and binders.
The plastic from oil gets used up. Oil out of the ground isn't replaced when you toss a plastic bottle. Because chemical reactions often produce heat as a by-product or require heat to start or as a catalyst, there is a net loss.
So other things being equal, choose metal or paper packaging over the plastic. Don't drink water from plastic bottles, carry a refillable aluminium bottle.