Actually the Centauro II with the 120mm gun does have stabilization for firing on the move. Otherwise you're basically claiming the same differences between a Leopard and Centauro as could be made between a Jagdtiger and a Hellcat.
Yes it's Wikipedia, but it claims "The Hellcat was the most effective U.S. tank destroyer of World War II. It had a higher kill to loss ratio than any other tank or tank destroyer fielded by U.S. forces in World War II."
M18 Hellcat - Wikipedia
Another key point of course is to not refer to a TD as a "tank". They have different and specific roles. A TD is meant to be used in the defence...massing fire from a larger number of cheaper platforms to overwhelm attacking tanks through volume of fire (with the added bonus of being able to provide direct fire support to infantry).
I'm certainly not suggesting that we adopt something like the Centauro INSTEAD of Leopards, but simply raising the question as to whether the argument made by the speaker in relation to TD's historical roles and the advantage of superiority in quantity of platforms possibly has some validity now as well.
If we are going on the assumption that the role of the CF in a European conflict would at least initially be in the defence (I'm assuming that we have no intention of invading Russia), then would it for example be beneficial to have a Regiment of TDs as part of our armoured mix instead of three Armoured Recce Regiments? Maybe a Tank Regiment for the attack, a TD Regiment for defence and an Armoured Recce Regiment for....well Recce.