Until the Beretta corporation bought controlling interest in Sako (and Tikka, combining them into a single manufacturer), the changes from "Firearms International", to "Garcia", to "Stoeger" were simply changes in the U.S. importer. However, it is true that a number of changes in the actual rifles occured more-or-less in tandem with the change in U.S. distributors.
The Riihimaki guns of the 1950's usually had rather nice wood with a lighter stain. When the "new generation" of "three-number" L-actions was introduced, the wood quality was similar, but they soon went to a much darker stain that I felt was not quite as attractive -- however that would be a matter of taste.
The original Firearms International Sakos had high luster blue jobs, even in the standard grades. They also had a slimmer, more svelte stock configuration and a lighter barrel contour. Shortly after the transfer of the line to Garcia, the manufacturer (presumably at the request of the importer) beefed up the weight of both barrels and stocks, and in an attempt to hold costs down during a period of a weakening dollar, toned down the blue on the standard grades to a lower polish. While all of this sounds like the Garcias were somewhat downgraded, that is not necessarily the case. I've seen some truly amatuerish checkering jobs on pre-Garcia guns that I've never seen on Garcias, and on the whole the wood was better on the Garcias (unfortunately, there was also a lot more of it). Still, because of their slimmer lines, I prefer the older guns, even thought he QC might have improved (at least in the wood department) on the Garcias.
When Stoeger took over from Garcia, they introduced what is commonly called an "oil" finished stock in the "Hunter" grade that supplanted the "standard" (however, I believe more accurately that it is a satin lacquer rather than oil). Stoeger also quickly changed over to the A-series actions. These were largely identical to the L-series except that they had a shrouded cocking piece. The blue of this model is somewhat more subdued than earlier guns, at least in the "Hunter" grade -- the Deluxe models have seemed to keep a very high-luster blue throughout.
I have no familiarity with the short lived S-series actions, but soon along came Beretta and introduced an entirely new action called the Model 75. The fit and finish of the Beretta era guns is excellent. This is in part due to sophisticated factory automation, but whatever the reason, their quality is very high. As begun under Garcia, there tends to be more difference in the blue and stocks between the "standards" and the "deluxe" models than seemed to exist in the "pre-Garcia" guns.
Insofar as performance, I have found no consistent difference in any of the iterations. I have FI's, Garcias, and Stoegers (and friends who have Berettas) and any is as likely to shoot as well as another.