Aluminum is typically not as strong as steel, but it is also almost one third of the weight. This is the main reason why aircraft are made from Aluminum.
Stainless steel is made up of iron, chromium, nickel, manganese and copper. The chromium is added as an agent to provide corrosion resistance. Also, because it is non-porous the resistance to corrosion is increased. Aluminum has a high oxidation and corrosion resistance mainly due to its passivation layer. When aluminum is oxidized, its surface will turn white and will sometimes pit. In some extreme acidic or base environments, Aluminum may corrode rapidly with catastrophic results.
Aluminum has a much better thermal conductivity (conductor of heat) than stainless steel. One of the main reasons it is used for car radiators and air conditioning units.
Aluminum is typically cheaper than stainless steel.
Stainless steel is stronger than Aluminum (provided weight is not a consideration).
Stainless steel is less reactive with foods. Aluminum can react to foods which may affect color and flavor.