What information does a net ionic equation give that a complete ionic equation does not show

The net ionic equation shows  the chemical species involve in chemical reaction while the complete ionic equation also involve the spectator ions.

Explanation:

The net ionic equation shows  the chemical species involve in chemical reaction while the complete ionic equation also involve the spectator ions. The net ionic equation state that whether precipitation is occur or not. If the chemical reaction have no net ionic equation it means all are in aqueous from not precipitation occur.

Consider the following example:

Balanced Chemical equation:

HClO₂(aq) + NaOH(aq) → H₂O(l) + NaClO₂ (aq)

Ionic equation:

H⁺(aq) + ClO₂⁻(aq) + Na⁺(aq) + OH⁻(aq) → H₂O(l) + Na⁺(aq) + ClO₂⁻ (aq)

Net ionic equation:

H⁺(aq) + OH⁻(aq) → H₂O(l)  

The ClO₂⁻(aq) and Na⁺ (aq) are spectator ions that's why these are not written in net ionic equation. The water can not be splitted into ions because it is present in liquid form.

Spectator ions:

These ions are same in both side of chemical reaction. These ions are cancel out. Their presence can not effect the equilibrium of reaction that's why these ions are omitted in net ionic equation.