Chlorine is both a sanitizer and oxidizer, MPS is just an oxidizer.
Both chlorine and MPS will burn up (oxidize) the organic debris in the tub. You can use either to do the job with chlorine duing a double duty at higher levels.
To keep your tub free from nasties you need a sanitizer (in this case chlorine). As the chlorine gets used up it forms combined chlorine (CC). CC is the stuff that makes the chlorine smell; in order to get rid of it you either need 10x free chlorine (FC) of the CC reading ( if it's 0.1 PPM CC then you need 1 PPM FC; if it's 1.0 PPM CC you need 10 PPM FC) to break the chemical bond of the CC or you can use MPS.
Just remember that you need a sanitizer in the tub ... MPS may keep the water looking clean for a while but the water probably is not as clean as you might think.
Something that I started doing every so often is to hit the tub with both MPS to oxidize and chlorine to sanitize, running 2 jet cycles with each back to back ... this simulates the enhanced shock that's being sold.
