One uses "think of the children" as an excuse to enact broader control over society. Witness kiddie porn being the argument against P2P and PGP, or trying to censor "satanic" or sexually explicit lyrics, or any of a litany of other such nonsense claims.
The other uses it to remind people that this shit actually, you know, affects the children.
With the kiddie porn issues, generally the number of children being talked about is a very small minority of the total, and usually the issue under discussion has only indirect possibility of helping those children.
However advertisement of poor food choices to children is something almost all children are subjected to on a daily basis, therefore when discussing regulation we can see that the majority of children will be beneficiaries.