A well designed strut bar will make a difference; however, it is not a difference that you will notice in day to day driving.

There's a reason that the ROTW DC2 ITR came with front and rear strut bars.

They help in radical handling situations (especially with uneven road surfaces) to even out the chassis flex that could cause an older car to behave in a less than optimal fashion.

They are not absolutely essential, even in racing, depending on what chassis you're talking about. For example, I happened to have noticed that the only 4G VTEC Prelude in Honda Challenge goes to the track very often without the front strut bar. I believe this is probably one of the Honda chassis most likely to benefit from a strut bar up front, but the driver is very stubborn.

I have never seen a G3 Integra go out without strut bars.

Not sure what all that means, but there it is. LOL....