If you put the environment tikzpicture inside a box, it has height 15.84369pt and depth 0pt, because the reference point is at the bottom border. Then TeX applies the usual interline algorithm, the next base line has distance \baselineskip.
In case of tabular, the default reference point is centered regarding the mathematical axis (\vcenter is used for vertical centering). The result: the height is 8.9pt and the depth is 3.9pt. If the usual algorithm for \baselineskip gives a inter line space smaller than \lineskiplimit, then TeX uses \lineskip instead (default is 1pt).
If you want similar spacing then the reference point of the tabular can be moved
downwards with the optional placement option b:
\documentclass{report}
\usepackage{tikz}
\begin{document}
\setlength{\abovecaptionskip}{0pt}
\begin{figure}
\centering
\begin{tikzpicture}
\node[rectangle] {Some Figure};
\draw (current bounding box.south west) rectangle (current bounding box.north east);
\end{tikzpicture}
\caption{A Caption}
\vspace{1cm}
\begin{tabular}[b]{|l|l|}
\hline
Nonlinear & 3.720894e-0\\ \hline
\end{tabular}
\caption{B Caption}
\end{figure}
\end{document}

Or in the other direction, the reference point of tikzpicture can be changed, e.g.:
\documentclass{report}
\usepackage{tikz}
\begin{document}
\setlength{\abovecaptionskip}{0pt}
\begin{figure}
\centering
\begin{tikzpicture}[baseline=(current bounding box.center)]
\node[rectangle] {Some Figure};
\draw (current bounding box.south west) rectangle (current bounding box.north east);
\end{tikzpicture}
\caption{A Caption}
\vspace{1cm}
\begin{tabular}{|l|l|}
\hline
Nonlinear & 3.720894e-0\\ \hline
\end{tabular}
\caption{B Caption}
\end{figure}
\end{document}

The extreme, without any space can be achieved by \nointerlineskip:
\documentclass{report}
\usepackage{tikz}
\begin{document}
\setlength{\abovecaptionskip}{0pt}
\begin{figure}
\centering
\begin{tikzpicture}[baseline=(current bounding box.center)]
\node[rectangle] {Some Figure};
\draw (current bounding box.south west) rectangle (current bounding box.north east);
\end{tikzpicture}
\nointerlineskip
\caption{A Caption}
\vspace{1cm}
\begin{tabular}{|l|l|}
\hline
Nonlinear & 3.720894e-0\\ \hline
\end{tabular}
\nointerlineskip
\caption{B Caption}
\end{figure}
\end{document}

[baseline]option to the Tikz picture and it should give similar results. And use[preview]option ;\documentclass[preview]{standalone}. – percusse Dec 13 '12 at 14:32