Suction-side cleaners work in conjunction with your pool's pump. They attach to the intake side of the pump, so the water passing through the cleaner picks up debris and deposits it into the pool filter. Suction-side cleaners are usually the least expensive option, but they depend heavily on your pump to do much of the cleaning job. If you don't have a powerful, efficient pump and filter, or if you have a large pool, this might not be the best choice for you.
Pressure-side cleaners also rely on your pump as they operate. These cleaners install on the output side of the pump, and the pressure of the water being pushed back into the pool is used to create a vacuum within the cleaner. Unlike a suction-side cleaner, a pressure-side cleaner has its own filter, so it doesn't pass debris into your pool filter. The pool pump alone may not be enough to power some cleaners, however, and you may need a supplementary booster pump if you opt for a pressure-side cleaner.
Robotic cleaners are the most expensive pool vacuum option, and they operate independently from your pool pump. They are self-powered with an electric motor, they move around the pool under their own power and they have their own filtration systems. Because they don't use the pool's filtration system, they don't put any additional strain on the pool's filter, and in fact they provide a secondary source of filtration. They are not entirely self-sufficient, however; they can't remain in the pool, and you'll have to remove them between cleaning cycles.
Using a suction-side or pressure-side cleaner requires that the pool pump run during cleaning, which is likely to increase your electric bill, and a pressure-side cleaner's booster pump will use even more electricity. These cleaners can also increase the load on your pump as they work, which may require you to install a larger pump than you would otherwise need or cause a variable-speed pump to run at a higher speed and consume more power. In general, robotic cleaners will use less electricity, since you won't have to run the pool pump during cleaning cycles. In terms of cleaning efficiency, robotic cleaners are the most thorough overall; suction-side cleaners excel at scrubbing pool surfaces, and pressure-side cleaners handle large debris well.