Sodium Sulfate vs Sodium Sulfite
The last statement


  …sodium sulfate and sodium sulfite are both basic and would turn pH indicator the same color


is true only for $\ce{Na2SO4}$ as it's formed by both strong base and strong acid and won't noticeably affect pH.
$\ce{Na2SO3}$, on the other hand, undergoes hydrolysis:

$$
\begin{align}
\ce{Na2SO3 + H2O &amp;&lt;=&gt; NaOH + NaHSO3} \\
\ce{2Na+ + SO3^2- + H2O &amp;&lt;=&gt; Na+ + OH- + Na+ + HSO3-} \\
\ce{SO3^2- + H2O &amp;&lt;=&gt; HSO3- + OH-}
\end{align}
$$

resulting in elevated pH (basic solution) up to 9 (according to Wikipedia).