Toby Nangle has written a very good post on pensions, pointing out that Pay As You Go (PAYG) pensions and fully-funded pensions are similar in that they both represent the old having financial claims on the young. We can fund their pensions through taxing the young or by having them own financial assets. In his words:

Pensioners will collectively consume output produced by the young. Money, as always, mediates – and so in place of ‘consume output produced by’, read ‘receive income from’. Pensioners will receive an income that can come only from non-pensioners. This income could be in the form of rent, dividends, and interest only from the young, or the proceeds of asset sales made only to the young. This income could be in the form of tax transfers only from the young. Or some mixture. It was ever thus and it will ever be thus.

This is true, and a good point. But he goes too far in implying that this makes PAYG pensions and funded pensions similar overall, or that deciding between these two socially only involves practical questions. There are two huge differences.

Inside a recession, when interest rates hit the 'Zero Lower Bound', extra consumption can increase aggregate demand. However, most of the time the economy is neither in a recession nor at the ZLB, and extra consumption comes at the expensive of extra saving (and saving is what goes into investment). Unless you are above the 'golden rule' level of saving—and this is very, very unlikely when there are so many taxes on saving and subsidies to non-saving (like providing retirement incomes) in our society—then extra saving (and investment) raises your productivity and living standards.Basically: if we force pensioners to save and invest to fund their retirements then when they actually do retire we have more capital, which means higher productivity and higher income. Thus, for any given level of retirement benefits, bearing it is an easier burden.
Governmental claims can only be on your country's own citizens. Financial go all around the world. If you save a lot in your youth, invest those savings in foreign capital, and that capital earns a return, then your pensioners' claims could be on the young working citizens of another country—possibly one with a growing population! (NB having claims on the youths of another country doesn't necessarily make them worse off; if foreign investment raised a factory or funded training that made those citizens more productive then everyone can benefit.) Of course, this second point doesn't question Toby's story as a model for the world as a whole, just when we're considering individual countries separately—and since this is how pensions tend to be considered this is probably the way we should look at the question.

Yes, PAYG and funded pensions both involve bundles of financial claims. Yes, they might both be the same size, and one main difference is simply how the system is run and intermediated. But it does not follow that other differences are small or trivial; PAYG is likely to lead to a lower level of saving, investment, capital and income. Under PAYG, the burden of the elderly is heavier, because we have narrower shoulders.