"MPS" stands for monopersulfate as in the chemical potassium monopersulfate. It is also called non-chlorine shock. It is an oxidizer and by itself is not a disinfectant. It may be used in hot tubs because when combined with silver ions as in the Nature2 system and at hot temperatures the combination can disinfect and has passed EPA tests. It's much more expensive than bleach, but its main advantage in a spa is that it lasts longer than chlorine so if you aren't soaking every day or two you can go a week without having to dose, even if you have an ozonator (with an ozonator, the ozone reacts with chlorine depleting it faster). That is, you dose after your soak, but don't usually need to dose again until after your next soak. With chlorine, you generally have to dose every day or two, especially if you have an ozonator.
There are quite a few people who only use their hot tubs on weekends and don't want to be bothered with having to add chlorine every day or two to their spa. If you are soaking every day or two, then chlorine is no problem at all since you have to add it after each soak anyway.