The nucleus of an Overline atom is typeset in cramped style. You get the same height of the prime in the denominator of a fraction:

\documentclass{article}
\begin{document}
\[
\frac{x'}{x'}
\]
\end{document}

You can see that the height of the prime in the denominator is the same as in \overline{x'}.

Normally this is desired, but your case requires remedy: use \cramped for the first x', but I also suggest adding \,.

\documentclass[twocolumn]{article}
\usepackage{mathtools} % for amsmath and \cramped

\begin{document}

Without \verb|\cramped|
\[
f(x',\overline{x'})
\]

With \verb|\cramped|
\[
f(\cramped{x'},\overline{x'})
\]

With \verb|\cramped| and \verb|\,|
\[
f(\cramped{x'},\overline{x'}\,)
\]

\end{document}

(I use twocolumn just to reduce the size of the picture)

You might force uncramped style by declaring \displaystyle

f(x',\overline{\displaystyle x'}\,)

Not what I'd like to see, to be honest.

The nucleus of an Overline atom is typeset in cramped style. You get the same height of the prime in a square root:

\documentclass{article}
\begin{document}
\[
\sqrt{x'}
\]
\end{document}

You can see that the height of the prime in the denominator is the same as in \overline{x'}.

Normally this is desired, but your case requires remedy: use \cramped for the first x', but I also suggest adding \,.

\documentclass[twocolumn]{article}
\usepackage{mathtools} % for amsmath and \cramped

\begin{document}

Without \verb|\cramped|
\[
f(x',\overline{x'})
\]

With \verb|\cramped|
\[
f(\cramped{x'},\overline{x'})
\]

With \verb|\cramped| and \verb|\,|
\[
f(\cramped{x'},\overline{x'}\,)
\]

\end{document}

(I use twocolumn just to reduce the size of the picture)

You might force uncramped style by declaring \displaystyle

f(x',\overline{\displaystyle x'}\,)

Not what I'd like to see, to be honest.