In the "having money" case, you have more options, but if you're given options, you also have more opportunity to make terrible decisions. And if it's a lump sum (or private investment of some kind), you can pass it on to your children - you can't do that with pensions in the other type.
On the other hand, in the current system as it's used in France, Germany etc, their incentive is that hopefully someone else will do it for them in 40 years. But from what I gather, very few members of GenZ believe that our pension system will survive in its current form until it's their turn to benefit from it. They expect it to collapse, so everything they'd now put in would be wasted, much like if you invest in something after it has signaled that it will default soon.
Consider this extreme edge case: If everybody is retired and no is is working, inflation goes to infinity and all those savings and stocks become worthless.