In general, pensions are a way to allocate society's aggregate income across generations - in a closed economy this would mean domestic production. Choosing a funded system relative to for example a pay-as-you-go system is basically a question of creating the right incentives for the financing of pensions. That is, paying pension contributions rather than taxes.
Funded pensions tend to be better at tackling demographic changes, and pay-as-you-go systems tend to be better at coping with large transitory shocks, e.g. large changes in inflation rates. A mixed system like the Danish one therefore seems to be a good solution to secure a decent consumption level at retirement.