I guess one of the main gains is the ability to colonize... everywhere. You can grow at a much more exponential rate than organics can (or, at least with a lot less effort since for them it would take micromanaging multiple species or sub species (which could lead to other problems) and maybe robots have new traits too? we don't know.
EDIT: I guess when i think about it. Less micro is one of the main gains. Since you can micro organics to be good at specific things (even better than synths at some things with the new traits) but synths are just overall really good at whatever you ask them to do.
1.Mod one planet to another preference.
2.Build a colony ship
3.Mod the planet preference on the planet back to prevent pops from dieing.
4.Repeat once for the third planet-group (wet, rocky, dry)
Congratulations, you can now colonize everything.
And with the tech you definitely have at the point you can build synths, your pops even have 100% habitability