They work in different ways to accomplish the same goal: better handling.

Strut bars work simply to stiffen the chassis by linking points together resulting in more rigidity. Increased stiffness = better handling.

Sway bars actually work like a large spring connecting the left and right suspension systems. When you take a hard corner, the sway bar will tie the left and right sides together transferring the force across the car to decrease body roll. The stiffer (in most cases the thicker) the bar is, the more weight transfer and the less body roll. There is some small degree of decreased ride quality, but not as much proportionally as stiffer coil springs would.

So you can get both. You'll feel the differences in the sway bar(s) before you would feel the strut bar...you have to push it a bit more to feel the difference in the strut bar.

For the upper front strut bar, I would get the Acura TL-S/CL-S bar, cheap and functional.

For the sways, you can either go mild with a TL-S/CL-S rear sway bar only (this will help reduce some of the stock understeer making the car handle better by being a bit more neutral). Or you could go all out and get an aftermarket kit with front and rear bars like Eibach, Comptech, etc.