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The entire car flexes a lot when turning, especially the strut mounting points (strut towers) since the struts are the main suspension components connecting the wheels to the chassis. The struts aren't connected to each other in any way, so they're free to flex and move independently. Tie them together with a 2 point strut brace (the most common) and it stiffens things up a bit. Only problem is, you just connected 2 flexy strut towers to each other, so now they flex together instead of independently.
Ok so that's a little better than it was with no brace. A 3 point brace connects the two strut towers together, and then anchors the bar to the firewall, which doesn't flex nearly as much as the strut braces since it's a large part of the unibody structure. This pretty much takes any flex out of the struts and lets the suspension do it's job better.
Having a powerful engine has nothing to do with it. The entire car is going to flex regardless of the engine's power output.
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