Escalators are stairways that run on electricity and are used for transportation purposes. The most common places where they are used are malls, railways stations, subways and airports. They are installed at places where a larger number of traffic is expected.
Escalators are relatively slower and you may take a longer period of time to move between floors.
Elevators operate vertically and are closed cabins to transport a certain number of people from one floor of a building to another. These are used in places where there is relatively less traffic such as hotels and high rise buildings.
Elevators use less amount of energy as they consume electricity only when they operate. They are also convenient for people who get tired easily and want to reach their destination quickly.