Which one improves handling better? Or do they work in different ways? If I were to get one over the other which one would I get...or do I get both?

 

sways over the strut of course. getting them both is obviously the best choice.

 

I would get the sways first, then decide for yourself if you need the Strut brace. Our car has one already, and adding another brace on top of that will make the body flex less. The sways are good for body leans in corners. The strut brace provides better turn in, not necessarily reduced body sways.

 

Get sways bars first! You will notice the difference on your handling, its stiffer and tight!