Well, they were quite different things. The Bersaglieri had been introduced in 1836, part of an effort to modernize the Army of the Kingdom of Sardinia with the introduction of a new specialty infantry corp focused on mobility, and on the rapidity of engagement and disengagement compared to standard infantry.

Their identity as a corp continued to be shaped by this accent on mobility, even if their operation range tended to widen a bit, after their usage during the wars of Italian Independence, to include police action and several instances of "ordinary warfare". During the Great War, it was the Bersaglieri who introduced bicycles in order to retain a maximum of quickness in their deployment, even if this will come more handy during the last months of the conflict.

Obviously, this meant that their role as "shock troops", that could have been achieved on level ground and under the assumption of mobile warfare, tended to decline during the Great War.

The arditi - on the other hand - were introduced in circumstances where mobility had been lost for the most part, and essentially remained in operation only during the last stages of the Great War. Their purpose was, more or less, to provide a new core of "assault troops", in part modeled on the German experiences during the same time frame.

Compared to the Bersaglieri, they tended to be more heavily armed - or, better, to have access to larger amounts of better equipment compared to the ordinary troops, and especially to make larger recourse to explosives. In terms of "heaviness", it is worth noting that their training continued to stress mobility, agility and physical prowess (even if several prominent Arditi could be reportedly physically impaired, it stands to reason that they were more of an exception), so that they tended to avoid being encumbered. The exemption from certain disciplinary regulations (for instance the chance to "personalize" their uniform), the volunteer enlistment, as well as the accent on the "elite" character of the Arditi seemed to encourage their high morale. It was often this "moral" and "morale" superiority over the rest of the troops that comes to be highlighted as one distinctive trait. In so far as their effectiveness, reports tend to differ, and it is clear that they could achieve impactful results when operating with a certain degree of tactical freedom, but tended to integrate poorly with the rest of the Army. The nature of their training itself seemed to encourage this "exceptional" collocation, and to reflect the desire of the Italian Commands to seek new experimental solutions, after struggling to introduce meaningful tactical innovations during the first two years of war.

I wrote two related posts - one and, if you scroll to the bottom, below the other wonderful contribution you might as well check out, two - dealing mostly with the political impact and legacy of the arditi but also adding a few technical details, that might be of some interest for you. Let me know if I can help with further questions, or more specific points that I might have left out.