Both have essentially identical breathing performance in the water, which is not surprising given that they use the same poppet design. (The poppet is slightly shorter in the X650 but is otherwise identical.)
Subjectively, I think the airflow is a little smoother with the X650 due to the direct path from the air barrel to mouth piece - it does not have to make the same bank shot off the flow vane that the air does in the S600.
In my experience, the X650 is a bit more reliable in very cold water. I have taken mine ice diving and other than the very rare ice chip being shot at you it gives no indication of icing, freezing, etc. In contrast the S600 has a tendency to develop a very slight freeflow in the same conditions.
I prefer the purge cover on the X650 to the S600 as I think it is easier to purge, but some divers prefer the S600 for the same reason, so it's a matter of taste and preference.
Bascially you can't go wrong with either one.
While you are at it though you might want to consider the G250HP. Internally it is identical to the S600, it just differs in the size of the case and dipahragm, and performance wise it is every bit as good as the S600, plus it has a better reputation in cold water.
The marketing pukes industry wide sing the praises of small second stages and how the lighter weight reduces jaw fatigue. It's true the G250HP is a little larger and heavier than the S600, but it's extra internal volume also makes it more bouyant which offsets the extra weight. Consequently I have never noticed any comfort difference between them in the water.
In truth, proper hose lenght and proper mouth piece design have a lot more to do with jaw fatigue than the weight of the second stage - but admitting that undoes over a decade of marketing campaigns. Personally, I think the appeal has as much to do with people thinking smaller is better (and more trendy) in a regulator just like they tend to think when talking about cell phones. Regulators are however not cell phones and smaller second stages introduce problems with smaller diaphragms offering less mechanical advantage and smaller exhaust tees that create more bubble interference.
So the G250HP will offer the same performance as either the X650 or S600 for a lot less money.