You can use a \mathstrut to give the both subscripts the same height and depth:

\documentclass{article}
\begin{document}
\begin{displaymath}
\sum_{\mathstrut j=1}^m \sum_{\mathstrut \langle i,j \rangle}
\end{displaymath}
\end{document}
A \strut is a vertical rule of zero width, so invisible, defined by latex each time a font is set, however these don't change with different parts of mathematics expressions such as subscritps. In mathmode the latex kernel defines
\def\mathstrut{\vphantom(}
which produces a vertical rule of the same height and depth as a bracket in the current math style, but again with zero width. Thus adding \mathstrut to an expression will guarantee that it has height and depth at least that of the bracket (. If your expressions have greater height, then it would be more appropriate to use \vphantom{...} with the ... a copy of the expression with most height.
\mathstrutdoes and where it get its size from? A static height or relative to something? Thanks. – LaRiFaRi Jul 08 '14 at 13:07\mathstrut. It says it is equivalent to\vphantom(– TonioElGringo Jul 08 '14 at 13:13\mathstrutwould be redundant if$($and$\langle$are of same height (they are) or disabling the "optimal" inter space if they aren't. No offence, your solution works perfectly. Just heard of that macro the first time... – LaRiFaRi Jul 08 '14 at 13:32\langleis about the same height and depth, and so the\mathstrutis not necessary on that term. However, adding it uniformly to both terms, produces a solution that will work with different content. – Andrew Swann Jul 08 '14 at 13:37