While I personaly do not use any of the power filters, they can and do serve a purpose depending on the type of marine aquarium kept. For reef aquariums I do not like the idea of any filtration that traps larger particles, which includes all of the planktonic life that is able to reproduce within my system. Keeping with the theme of being a reef, I like the idea that all the copepods, worm swarmers and the other multitudes of life forms are able to remain within my system and feed my corals, as well as their being able to perform their main functions of house cleaning. For fish only systems, or for nano tanks, a power filter can help with providing a bacterial biofilter that will colonize the filter's padding and with their high rates of water flow, make for a handy place to run carbon as well.
For small "nano" tanks, a suitably sized hang on, or cannister filter can be the only way to provide such small tanks with filtration and water flow. As with any filtering mechanism, the filtering material must be cleaned on a regular basis to avoid having the trapped orgranic matter decay and cause water quality issues within the system. It is for that reason alone that if I were to use a power filter, it would be the hang on the tank type simply for being the easiest to clean. I have found that if I have to tear apart a cannister filter and put up with the usual mess that goes with doing that, I am highly unlikely to perform the much needed cleaning on a regular basis. Where as, a hang on type, with its easy access to the filter pad, makes it much more likely that I will actualy clean it on a regular basis.