Just had a jury return verdict of guilty on aggravated assault and lesser included of misdemeanor assault. Which verdict should prevail and what's the case law?

Maybe the verdicts conflict and cannot be accepted until the conflict is removed. If the jury has already been discharged then the verdict is not necessarily invalid, but probably will only support a judgment on the lesser offense. See Moranza, 913 S.W.2d at 724; Sauceda, 739 S.W.2d at 376.

I am assuming the conflict is that the defendant caused serious bodily injury and (impliedly) only caused bodily injury or used a deadly weapon and (impliedly) did not use a deadly weapon.

The judge sent them back and made them fix it. Guilty of Murder and Aggravated Assault.