Value of Adult Lives vs. Children's Lives

In quite a large number of societies around the world, including contemporary American society, most people seem to place a higher value on the lives of children, especially infants, than they do on the lives of adults.  Particularly when considering the controversial issues of euthanasia and abortion, this ranking of values seems important to analyze and subject to possible revision.

A large part of the exceptionally strong aversion to killing infants felt by many people is likely evolutionary - protecting one's own young aids in passing on one's genes to the next generation, and that can be extended to protecting a relative's young, and perhaps even to any young in one's own species.  A similarly sized part also seems to be societal, possibly related to religion - more than one religion asserts that children are born innocent, 'without sin' so to speak, and so are inherently better, somehow, than those people who have lived for long enough to have transgressed against whatever doctrines the religion contains.

However, while I agree that killing infants (fully sentient infants, as opposed to non-sentient fetuses) is indeed something that people should avoid doing, I would argue that killing slightly older children or adults is actually worse morally speaking in most circumstances in which the primary variable is the age of the person dying.  This is because infants have only potential; it is not guaranteed that they will have good or enjoyable lives.  Adults (at least most adults who are not suicidal or severely depressed) not only have potential, but also have something to lose - namely, anything they have enjoyed so far in their lives which is possible to keep enjoying (a hobby, a fun career, friendships and other relationships).