It's a personal taste issue.

Suction side cleaners are the simplest. You fill the hose with water and stick it in the hole under the skimmer basket. Junk gets trapped in the pump's basket and in the filter. It can be a manual vacuum you push around or an automatic cleaner.

Pressure side cleaners work by using the return water to power them. Things like the Polaris 165 use the water to power the piece that floats, but also the water is routed down to a piece on the bottom. The water drives that piece backwards like a jet, but there's a bag back there to catch the stuff it blows. They tend to be far more powerful and can be more effective than suction, but the bags don't catch the finest stuff. I just put a handful of cotton balls or a 6"x6" square of sheet cotton (from a drug store) in and it catches the fine stuff.

I don't know much about auxiliary pump cleaners.

Generally, my experience has been the pressure side cleaners seem to work better and more effectively than suction side cleaners, but others my well prefer suction.

Robotic cleaners, when they work, (!) are the best by far.