Funded versus unfunded state pensions. Pro's, con's, and hybridization.?

Hello! I've been curious as to the pro's and con's of funded and unfunded (PAYG) state pensions, and how one would go about determining what a reasonable mix is in relation to the economy of a particular nation. I love in Canada and we have a nearly fully funded state pension system is my understanding, and given the benefits of it, I can't understand why any nation with a stable economy would refrain from using such a system. My reasoning is simply that you peg your PAYG pension payments to compensate for risks on funded state pensions investments, but so long as the national economy can be reasonably said to be stable and have long-term growth viability (and the investments are safely diversified), I can see why anybody would not use some form of funded state pensions as the basis of the bulk of state pension payments. I'm not an economist, so this mystifies me somewhat, and I hope there are some economists here who can clear things up. Additionally, what are some of the various schemes that have been devised to equalize risk amongst the workforce's state pension contributions, and how do they compare?