From personal experience:
Took my year old son to Sweeden on AA. Wife flew on a business award ticket, I flew on a coach purchased ticket. Options for my boy:
Purchase a coach seat for him (50% of my coach fare)
Allow him to travel as a lap child in coach (10% of my coach fare)
Allow him to travel as a lap child in business and hope for an open seat (10% of the current business fare, even though my wife was on an award ticket).

I ended up purchasing him a coach ticket, but since there were only 5 in business, he sat with my wife on the way over.

Don't want to start a flame war over children (babies) in premium cabins. My son sleeps from 10 minutes after take off until landing, doesn't need attention from the FA (better service for other pax) doesn't get drunk, and leaves an extra meal selection for everyone else. He has is own gold AA card and is entitiled to upgrades just like everyone else.

PLEASE MAKE SURE YOUR CHILDREN HAVE THEIR OWN SEAT. They are more comfortable in familiar surroundings, and much safer.

Just my $0.02.