Automatic Pressure-Side Cleaners
This type works off of water pressure coming from a pump. The pump can be your main circulation pump, or it can be from a dedicated (booster) pump. A pressure-side pool cleaner runs by water pressure from the the pump that drives the cleaner around the pool and is also what forces the debris into the bag (that holds the debris). The most beneficial thing about a pressure-side pool cleaner is that it doesn't suck stuff into your pool filter or pump basket (allowing you more time in between cleanings). If your pool is around a bunch of trees, or if you get a lot of debris in your swimming pool, than a pressure-side pool cleaner is the best way to go.
Pros of a dedicated pump - are, your cleaner is probably going to clean the pool a little better (than a non-dedicated pump) and will also last longer because a non-dedicated pump can lose efficiency when your filter gets dirty and it also always runs when the main pump is on (causing premature wearing of the pool cleaner).
Pros of a non-dedicated pump - are, they're cheaper to install. Without having to install a dedicated line and a separate booster pump, you don't have to worry about the additional expenses. And in most cases, the pool cleaner is a little cheaper too.
Cons of a pressure-side pool cleaner - includes not being able to filter small particles through the bag and it also doesn't scrub the walls very good. Also, unlike suction-side pool cleaners, they (pressure-side cleaners) don't act like a moving drain (read further for more information).
Automatic Suction-Side Cleaners
These rely on suction to make them move and vacuum the stuff off of the pool floor. There are several advantages to this. First, as I mentioned before, is that they act like a moving main drain. When the cleaner is underwater, sucking stuff into it, it is also sucking water through your filtration system, causing you to turn more water over in a shorter amount of time.
Some suction side cleaners have the ability to "scrub" your pool walls. By agitating itself as it moves around the pool, it also scrubs the walls. This can possibly cut down on the number of times you need to brush your pool. And since it sucks stuff right into your filter, it can remove much finer particles than a pool cleaner with a bag. And since there is no need to install any additional plumbing or pumps, a suction-side pool cleaner is usually a lot cheaper to install. If you are in an area where large debris rarely gets into your pool, then a suction-side cleaner may be your best bet.
Cons of a suction-side cleaner - First, as I have already pointed out, they suck stuff strait to your filter and pump basket. This can be a real nightmare if you live where there are a lot of trees. The only thing you can do about this is to buy a leaf trap that catches the big stuff before it ever even gets to your pump basket. Another thing that can greatly effect your suction-side pool cleaner is your filter. Without a clean filter, your pool cleaner can suffer dramatically, since the cleaner relies on the suction from your main pump to drive it around the pool and vacuum stuff up.
Robotic Automatic Pool Cleaners
These are driven by electric motors inside the unit. The electricity that powers the cleaner comes from a little transformer that you plug into a outdoor GFCI outlet. The transformer converts the outlet electricity to a low voltage which is then connected to the cleaner via a long cord.
It vacuums stuff strait into its own filter by a separate pump inside the unit. It also usually has some sort of on board computer chip that diagnosis any issues with the cleaner and helps to "learn" the shape of the pool. Some even have a remote control that allows you to maneuver the cleaner around your pool to spot clean anything it may have missed.
Robotic pool cleaners are one of the best when it comes to small debris and sand or silt situations. It is one of the only type of pool cleaners that not only scrubs the walls, but also the tile line. They also serve as a great supplemental way to circulate the water in your pool because of the powerful pump inside that vacuums the debris. While they are among the most expensive type of pool cleaner on the market, they can make a great investment in the right situation.
Cons of a robotic pool cleaner - With a price range of $700 to $2000+, they are expensive. Hopefully it never brakes because if there is ever an issue with the cleaner, chances are you'll have to mail it off to the factory or an authorized service station for it to be fixed. Also, most manufacturers recommend that you remove the cleaner from your pool each time you use it.
There you have it, the different types of automatic pool cleaners and what the pros and cons are of each. I hope that helps you in making a decision on which automatic swim pool cleaner Is right for your swimming pool.