Having just had a newborn, I can tell you they sleep for preposterously long periods of time, and will quite happily sleep through loud noise. When they do wake, they only cry until their immediate needs are met..i.e food, being winded, change of nappy etc.
I think the saying also includes a suggestion of 'innocence'. In other words, a baby's sleep is clearly untroubled by the impact of the previous day's activities or by the nightmares arising from the bad thoughts/actions older people might suffer from.
I echo QM's response, and would have put my version first if my PC wasn't playing up. As adults, we see babies sleeping and the site is constantly fascinating, and does indeed give an impression of carefree slumber, which it no doubt is. The fascination pales as children grow, and no-one seems very interested in watching adults snooze.