Normal hybrids 1-out-of-10 through normal hybrids 10-out-of-10 is just the hybrids scaling up in magnitude (basically, how many you will see in the game).
Advanced hybrids 1-out-of-10 adds some higher level maturity and modules they can get to.
Iirc, advanced hybrids 2-out-of-10 adds the first level of "the dyson plot",
Iirc, advanced hybrids 4-out-of-10 adds the second level of "the dyson plot",
Iirc, advanced hybrids 7-out-of-10 adds the final level of "the dyson plot" (the one that is basically game-over if you don't stop it before it happns)
and each level of advanced hybrids give them a bonus on their "central bank of pain" point accumulation, which currently goes only towards spawning the super-hybrid that can do the dyson plot (the super-hybrid can still spawn with advanced hybrids at 0/10 if normal hybrids is > 0, but it's just a particularly buff hybrid there).