I believe Donnie is spot on here in that you can't make a broad-brush assumption about the specific handling impact due to adding a strut bar in terms of over/understeer. Having a stiff structure for the suspension to transmit its loads with minimal deflection of the suspension geometry (mounting points) is the goal. Actually having the lowest possible, within reason, deflection of the whole chassis between each side and front to rear is what everyone wants (and gets with the modern roll cages constructed these days).
I'm most familiar with BMW sedans over the past 35 years of driving/autocrossing/tracking/etc, and prior to the late 90's, strut bars were useful in stiffening up the front structure -- especially on cars from the 1970s-1980s. However, on "modern" BMWs (which for the purposes of structure design I'm referring to the E39 5-series and newer since that was the model they leaped forward on with body structure design) I remain skeptical of the benefit to the average user, if any, of a strut brace for the vast majority of those purchased (i.e. typical street driving and even track events). These body structures are so stiff, in both torsion and bending, that I'm guessing (gut feel) that the addition of an expensive strut bar is of little measurable performance benefit.
I've challenged a number of the makers of these things to show real engineering data (i.e. Dinan for one since Steve has the knowledge and ability to instrument a car and interpret the data) on a strut bar in a modern BMW chassis, but NOBODY in the industry will respond. The process wouldn't be too hard: strain gages on the strut bar for example could be used to measure loads in real-time for example, and even an optical system could be rigged perhaps to measure tower deflection w/o a bar in place, etc.
The net of it is that nobody has any real engineering data showing the usefulness, or lack thereof, of a strut bar on modern BMW (and other makes as far as I know) structure. There is no reason for them to do this I suppose since if the data proves there is no benefit to handling, their whole marketing plan goes out the window since "everyone" flocks to these things like crack in the current market.
If anyone is interested in structure stiffness (torsion and bending) of BMW 5-series over the past 4 generations, check out this link:
http://www.autosteel.org/AM/Template.cfm?Section=PDFs&TEMPLATE=/CM/ContentDisplay.cfm&CONTENTFILEID=3632
Page 6 shows the significant leap in structure stiffness at the E39 point in time (due design, steel used, and manufacturing technique improvement allowing these to be implemented)...it is shown in terms of the body structure natural frequency increase in bending and torsion.
OT, but page 12 has an interesting look at the difference in high strength steel used between the E46 3-series on the far left and the E90 3-series on the far right.