So is there a particular kind of distortion that is better than another? If I just crank up the channel mixer, it seems like it'll be a lot different that if I use Saturn to beef the sound up until it touches the red.
Not sure about cranking up the channel mixer, because inside your DAW the sound information is represented as it is and will always be, so no software clipping will appear ever, unless a sort of limiting is applied by default (on FL Studio 12 there is no clipping while you are inside the DAW). Clipping appears when you render sounds which are over 0Db, and the simple action of rendering generates a compressed file, which means you lose the information above 0Db, which means that information missing is now become clipped sound.
Edit: didn't see it while I was writing this, but the post above explains this concept correctly.