Again, we're not doctors, but here are some general thoughts on mood stabilizers:
Lithium is the gold standard for treatment of BiPolar (BP). An estimated 70 to 80 percent of bipolar patients have a positive response to it. But it is thought that "rapid cyclers" may not to do as well on Lithium as other mood stabilizers.
Depakote works very well for mania and mixed states. My own kids became irritable and depressed on Depakote, but their illness tends more to depression than mania.
Tegretol is an effective treatment for acute mania and works to prevent future episodes of bipolar illness. I actually don't know all that many kids on Tegretol.
Trileptal is an anologue of Tegretol, meaning it is structurally similar but differs slightly in its compositon. Its effectiveness is still being evaluated for children. My son's psychiatrist said he did not believe it would be strong enough for an adolescent boy.
Lamictal works best on the depressive end of BiPolar (BP). It is FDA-approved for the longterm maintenance of BiPolar (BP). My own kids have done very well on it with zero side effects.
FWIW, my 13-year-old daughter has been stable on a combo of Lamictal and Lexapro for more than a year. In fact, we are reducing her Lexapro in the hopes of keeping her on Lamictal monotherapy.