Making a long table continue over two columns

Use the \twocolumn format, then you can use the package supertabular

\documentclass[11pt,a4paper]{article}
\usepackage{supertabular}

\begin{document}
\twocolumn
\tablehead{Header of first column & Header of second column \\}

\begin{supertabular}{ccc}
Table cell 1, 1 & Table cell 1, 2 \\
Table cell 2, 1 & Table cell 2, 2 \\
Table cell 1, 1 & Table cell 1, 2 \\
...
...
\end{supertabular}

\end{document}

together with the package multicols you can only use the tabbing environment.

A way to use longtable within multicols is described in one of the answers to Balancing long table inside multicol in LaTeX. As multicol does balancing after the table is processed some of the features (like repeated table headings) will not work though.

A way to use supertabular with multicols is described in Trick Supertabular into Multicols in new command.

The difference between the two table environments is that supertabular is calculating the table cell width anew for each column while longtablekeeps them uniform.

I already posted this answer in a similar question, but I used minipage and vdots and got the effect I wanted:

\documentclass[11pt]{article}
\usepackage{booktabs}
\begin{document}

\begin{table} 
\caption{Your Caption}

\begin{minipage}{0.5\textwidth}
\begin{tabular}{ccc}
\toprule
\textbf{Cell} & \textbf{Simulation} & \textbf{Theoretical} \\
\midrule
0  &  0.0  &  7.88e-31   \\
\vdots & \vdots & \vdots  \\ 
\bottomrule
\end{tabular}

\end{minipage} \hfill
\begin{minipage}{0.5\textwidth}
\begin{tabular}{ccc}
\toprule
\textbf{Cell} & \textbf{Simulation} & \textbf{Theoretical}  \\
\midrule
\vdots & \vdots & \vdots  \\
99  &  0.0  &  7.88-29  \\ 
\bottomrule
\end{tabular}

\end{minipage}
\end{table}
\end{document}