Samsung has denied the allegations that it is slowing down its older phones. The company already stated as much weeks ago but the investigation in Italy was opened based on user reports.

"Samsung does not provide the software updates to reduce the product performance over the life cycle of the device. We will fully cooperate with Italian Authority for Market and Competition's investigation in Italy to clarify the facts."
Apple (which admitted to downclocking older iPhones) is in hot water in the US, France and Italy, but Samsung is facing investigation only in Italy so far. The cause of the lowered performance in Samsung’s case is not clear.

For iPhones it was the chipset – as battery capacity drops, the phone becomes more likely to suffer a brown out when the chipset clocks up due to a demanding task. But we’ve seen slowdowns come from elsewhere too. For example, the original Nexus 7 was notorious for becoming sluggish as its flash memory aged (and the TRIM support didn’t entirely fix the issue).