In my document, the TikZ pictures have different bounding boxes so the two subfigures have staggered captions.
\documentclass{article}
\usepackage{standalone}
\usepackage{subcaption}
\begin{document}
\begin{figure}
\centering
\begin{subfigure}{.4\linewidth}
\centering
\includestandalone{one}
\caption[short]{long}
\end{subfigure}
\begin{subfigure}{.4\linewidth}
\centering
\includestandalone{two}
\caption[short]{long}
\end{subfigure}
\end{figure}
\end{document}
Since you wont have my two standalones, I will show what is happening:

I would like for the subcaptions to start on the same row.

supcaption. See, for example, the visual on p 6 of thesubcaptiondocumentation when using\subcaptionbox. If you replace your\includestandaloneby something like\includegraphics[height=3\baselineskip]{example-image-a}and\includegraphics[height=2\baselineskip]{example-image-b}, do you still have mis-alignment vertically? – Werner Aug 07 '13 at 22:42