The only octave effects that I have experience with are the ones on the DigiTech RPxx multi effects devices. Since I am more of a rhythm player (chords mostly), I don't get much use outta them. Some time back in the 80's I tried a stomp-box one (don't remember what brand), only did one or two octaves below the note, didn't track chords well at all. Heck, even the RP90 effect does not track chords well! They can do ok for single note lines like solos or where the bass doubles the guitar line. With the RP90, it will do one or two ocaves above, as well, can be used to "emulate" a 12-string guitar with a 6-string, but not perfect due to the high B and E stings played an octave up (unison on a real 12-string). I get better results with a chorus.
Fun to play around with, but seemingly (to me) not very usefull.
Just thinking, one good application (not "true" application) is the octave-fuzz devices, such as the Octavio or the MXR Blue Box Fuzz, etc... Not a true ocave, but due to the circuit and the clipping, it kinda gives an "octave up overtone" to the sound. Something to think about...
Cheers!