LH child awards are 75% of the adult miles when redeemed on LH/LX/LO/OS.
Whereas child fares tend (not always) to accrue full miles into the child's LH account.
Also, adult can spend miles from adult LH account on child's award tix, and vice versa (child can spend miles from child LH account on adult award tix.)
Of course, I am the legal guardian of my children, so I am the de facto owner of their miles anyway!
Taxes are generally (not always) less for child tix too, at least in Europe & Asia.