Depends.
People with money, good jobs, education, and some understanding of finance... tend to do a better job.
When it comes to between everyone else and government... It's more a matter of who will get it done at all.

Social security is crappy to live off of. But if it's all you have- like if you're a low wage worker, someone unlucky in investments, encountering a profoundly expensive unanticipated crisis after retirement, disabled, a homemaker with an ingrateful/irresponsible dead breadwinner, or... hell, just bad at planning (like most people, actually)... then it beats the hell out of nothing- or depleting your family's ability to save for retirement.

Personally I think SS should be changed into a simple disability/old age insurance program that either pays everyone some flat amount at a certain age or when disabled... or only pays the disabled or people in certain special circumstances.
The latter, of course, would also require some form of mandatory savings and investment for workers. Or at least automatic (perhaps people could opt-out if they insist, but it should require work to do so).

Expecting the norm of humanity to be abnormally interested in finance, long-term thinking, good at predicting, and aware of everything... is really setting yourself up for disappointment.
Especially consider that saving is even more difficult for the poor- who are less likely to be abnormally finance-savvy... and also more likely to retire from a broken body rather than because they can afford to.
And no one who is not independently wealthy at a young age can prepare for disability.

There has to be some safety net. Maybe Social Security has mutated too much (in our minds mostly) into something wrong. After all, it is only intended to be a safety net and many treat it like it's a full-on retirement program- these people either don't realize how crappy the payments are... or don't expect to live to retirement... or, like most people, don't think about it until it's getting late.

But I can see where there are some issues... After all, why should the middle classer who wasn't thrifty get a higher payment than a poor person who couldn't save or someone who was disabled? Just because of being used to a better lifestyle? BS. They should get the same tiny payment and live in an apartment if they didn't save.

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"Conservatives say if you don't give the rich more money, they will lose their incentive to invest. As for the poor, they tell us they've lost all incentive because we've given them too much money."

-George Carlin