The IEEEeqnarray environment is bulky, but powerful. It lets you have several aligned columns, and it also gives you the proper spacing around your = and \Leftrightarrow signs.
\usepackage[retainorgcmds]{IEEEtrantools}
\begin{document}
\begin{IEEEeqnarray*}{rClCrCl}
aaa & = & bb & \Leftrightarrow & cccc & = & dd
\\ e & = & f & \Leftrightarrow & g & = & hhhhh
\end{IEEEeqnarray*}
\end{document}
Output:

IEEEtrantools is well-maintained, but notoriously hard to install. This StackExchange question provides a good guide to the process of installing it properly, but a completely workable option is just to download IEEEtrantools.sty from here and leave it in the same folder as your code.
\Longleftrightarrowto be aligned at the equal sign, and my solution delivers this. However, if OP wanted the equations to be center-aligned, regardless of the connectives, then your solution (or Werner's) will be more appropriate. – Herr K. Apr 28 '16 at 16:52