Electrolysis of water: Which equations to use? (IB Chem)
For the acidic electrolysis, use the reactions where $\ce{H+}$ occurs.    

As $\ce{OH-}$ is not available in considerable amount there as a reagent, neither it is created as a product.    

Generally, for a reaction choice, apply the principle of availability and stability, allowing for a reagent to exist in (relative) abundance.
$\ce{OH-}$ or anions of weak acids like $\ce{ClO-}$ do not survive in acids. Acids do not survive in hydroxides. 

But note that using reactions with half of a molecule is not necessery.

$$\begin{align}
\ce{O2(g) + 4H+(aq) + 4e-  &amp;&lt;=&gt; 2 H2O(l)}\\
\ce{2H+(aq) + 2e- &amp;&lt;=&gt; H2(g)}
\end{align}$$

For the alkaline electrolysis, similarly, use the reactions where $\ce{OH}$- occurs.

$$\begin{align}
\ce{2 H2O(l) + 2e- &amp;&lt;=&gt; H2(g) + 2 OH^-(aq)}\\
\ce{O2(g) + 2 H2O(l) + 4e- &amp;&lt;=&gt; 4 OH^-(aq)}
\end{align}$$