g in Long has a depth where as in Short no letter has depth. This is why the misalignment comes. To correct it, you may add a \vphantom{g} to Short or \smash the Long (or only g).
\documentclass{article}
\usepackage{pbox}
\begin{document}
\hrule
\pbox[c][20pt][b]{\textwidth}{TEXT\\ \vphantom{g}Short}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ Long Text}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ \vphantom{g}Short}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ Long Text}%
\hrule
%
\bigskip
%
\hrule
\pbox[c][20pt][b]{\textwidth}{TEXT\\ Short}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ \smash{Long} Text}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ Short}%
\pbox[c][20pt][b]{\textwidth}{TEXT\\ \smash{Long} Text}%
\hrule
\end{document}

g. Why not use a standard\parbox? – David Carlisle Jan 25 at 12:02\pboxis pushed at the bottom, as requested by the final[b]argument. All boxes have the same total height, so this is what you get. Do you want\pbox[c][20pt][t]instead? – egreg Jan 25 at 12:05g, I should have seen that. @David: I use\pboxinside tikz to position a vertical line centered below the boxs. I don't know the widths. – Frank Seifert Jan 25 at 12:10