Position two stacked tikz matrices

A matrix is just really a node, so if you name the top matrix (Top) then you can use below of=Top in the other matrix to position it:

Code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix  [matrix of nodes,row sep=-\pgflinewidth,column 2/.style={nodes={rectangle,draw,minimum width=3em}}] (Top)
{
0   & 6 \\
};
\matrix [matrix of nodes,row sep=-\pgflinewidth,column 2/.style={nodes={rectangle,draw,minimum width=3em}}, below of=Top]
{
1   & 3 \\
};
\end{tikzpicture}
\end{document}

You can also use a scope and shift the entire content.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix [matrix of nodes,row sep=-\pgflinewidth,column 2/.style={nodes={rectangle,draw,minimum width=3em}}]
{
0   & 6 \\
};
\begin{scope}[yshift=-1cm]
\matrix [matrix of nodes,row sep=-\pgflinewidth,column 2/.style={nodes={rectangle,draw,minimum width=3em}}]
{
1   & 3 \\
};
\end{scope}
\end{tikzpicture}
\end{document}