Well, they are 2 totally different things. You can use both together. One is not used in place of the other.
Front and rear sway bars (more correctly: anti-sway bars) attach to the suspension to reduce body sway/lean when cornering. They are basically a torsion spring between the left and right sides of the car trying to keep the body level in a corner.
A strut bar is a bar that connects the tops of the front (and sometime also the rear) strut towers. The strut bar(s) reduce flex in the strut towers when cornering to keep the suspension from moving in relation to the body. A strut bar is more of a brace to structurally support the strut towers.
For a street car, slightly larger sway bars will help cornering while making the suspension slightly stiffer. Strut bars do little in street cars but can also help a racecar corner better.
You can get sway bars custom made. Amateur racers running front wheel drive cars use 32mm hollow rear swar bars with a much smaller, but still stiff front sway bar. This, along with stiff springs, is the only way to get a FF car to rotate similar to FR car.
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