The way text/boxes are laid out is to use a minimum spacing of \baselineskip between two consecutive baselines, or \lineskip between the lower and upper boundaries of two boxes (whichever is larger).
One way to achieve a relatively constant spacing is to place the baseline for the first minipage at the bottom and the baseline of the second minipage at the top.
Another way is to start and end every minipage with a \strut.
In the case of enumitem, adding \strut or \null produces way too much space between the two minipages. Instead you just need to add about 12pt of space between the default minipages (less if you add a \strut to the last \item). I'm not sure precisely how enumitem comes up with this 12pt, but this is my best guess.
It should be noted that text inside a minipage is not stretched or squeezed in order to fit the bottom of the page. You will also need to use \raggedbottom or throw in a \vfil somewhere, or put both minipages inside a common \vbox.
Demo:
\documentclass{article}
\usepackage{paracol}
\usepackage{enumitem}
\begin{document}
\begin{paracol}{2}
\noindent
\begin{minipage}{\columnwidth}
\begin{enumerate}[series=test1]
\item One
\item Two
\end{enumerate}
\end{minipage}
\begin{minipage}{\columnwidth}
\begin{enumerate}[resume*=test1]
\item Three
\item Four
\end{enumerate}
\end{minipage}
\switchcolumn
\noindent
\begin{minipage}{\columnwidth}
\begin{enumerate}[series=test2]
\item One
\item Two\strut
\end{enumerate}
\end{minipage}
\vskip\partopsep\vskip\itemsep\vskip\parsep\noindent
\begin{minipage}{\columnwidth}
\begin{enumerate}[resume*=test2]
\item Three
\item Four
\end{enumerate}
\end{minipage}
\bigskip
\switchcolumn*
\noindent
\begin{minipage}{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\begin{minipage}{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\switchcolumn
\noindent
\begin{minipage}[b]{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\begin{minipage}[t]{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\bigskip
\switchcolumn*
\noindent
\begin{minipage}{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\begin{minipage}{\columnwidth}
We need at least two lines here in order for this to work, so I hope that this is enough.
\end{minipage}
\switchcolumn
\noindent
\begin{minipage}{\columnwidth}
\strut
We need at least two lines here in order for this to work, so I hope that this is enough.
\strut
\end{minipage}
\begin{minipage}{\columnwidth}
\strut
We need at least two lines here in order for this to work, so I hope that this is enough.
\strut
\end{minipage}
\bigskip
\switchcolumn*
\end{paracol}
\end{document}
