If the source material that you're playing has the same number of channels as you have set for output, there's no difference between them. If those two number differ, the JRSS mixing option will up or downmix as necessary, but the no mixing option won't.
So, for example, if you have a stereo system (two speakers), and you play a movie that has a 5.1 surround audio track, JRSS mixing will downmix the 6 channels to 2 channels so you don't lose any content. If you set it to no mixing, you'll only get the two front surround channels coming out of your speakers, which means you won't have much of the dialog (or bass).
The only time it really makes sense to set it to "no mixing" is if you plan to do the up or downmixing yourself in the parametric EQ block.
