Two images to fill one beamer frame: most appropriate method?

You can use the standard \includegraphics command setting the proper values for the width and height in terms of \paperwidth and \paperheight; a box (in this case \makebox) will prevent an overfull box; using plain for the frames will remove the headline, footline:

\documentclass{beamer}
\usepackage{graphicx}
\begin{document}
\begin{frame}[plain]
\makebox[\linewidth]{%
  \includegraphics[width=0.5\paperwidth,height=\paperheight]{cat1}%
  \includegraphics[width=0.5\paperwidth,height=\paperheight]{cat2}}
\end{frame}
\begin{frame}[plain]
\makebox[\linewidth]{%
  \includegraphics[width=\paperwidth,height=0.5\paperheight]{cat1}}\\\nointerlineskip
\makebox[\linewidth]{%
  \includegraphics[width=\paperwidth,height=0.5\paperheight]{cat2}
}
\end{frame}
\end{document}