this is not an answer, but a demonstration of possibilities.
the code shown in the question doesn't exhibit the described result, namely
that the left angle bracket is larger than the right one.
edit:
since the request was for a smaller set of brakets, i've added examples showing
that the shapes used around the q are the smallest default size. to get
smaller ones, one has to go to ridiculous lengths, explicitly specifying a
different (and inappropriate) size.
\documentclass[12pt]{article}
\usepackage{braket}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\bra{\vec{q'}}\ket{\vec{q}} \quad
\bra{\vec{a'}}\ket{\vec{a}} \quad
\bra{a'}\ket{a} \quad
{\scriptstyle \bra{{\textstyle{a'}}}\ket{\textstyle{a}}}
\end{equation*}
\begin{equation*}
\bra{\vec{q}\,\smash{'}}\ket{\vec{q}\,} \quad
\bra{\vec{a}\,\smash{'}}\ket{\vec{a}\,}
\end{equation*}
\begin{equation*}
\bra{\vphantom{a}\smash{\vec{q'}}}\ket{\vec{q}\,} \quad
\bra{\smash{\vec{a'}}}\ket{\vec{a}\,}
\end{equation*}
\end{document}

note that the coding here isn't good style -- never use multiple adjacent equation environments. and i've also taken liberties with spacing,
since it's not really clear what is wanted.
edit:
it has come to my attention (by way of a comment on Increase in bracket sizes due to power symbol) that the physics package also supports the \bra \ket notation, and according to texdoc physics you can apply a * to suppress automatic sizing (see page 6).
\documentclass[phys]? If possible, try to give an example with\documentclass{article}.physis not known to me, where do you have it from? And the []-notation looks wrong. Should be {} – LaRiFaRi Aug 17 '16 at 14:20\documentclass{article} \usepackage{braket}and the size of the\braon the left side is the same size as the angle bracket on the right. so you must have something more complicated that we aren't seeing. (i do find it unpleasant that the arrow on the right is bumping into the closing angle bracket.) – barbara beeton Aug 17 '16 at 14:48\ket{\vec{q\vphantom{'}}, maybe it can help in time of searching for better solution :-) – Zarko Aug 17 '16 at 14:54\smashwould be more appropriate. – barbara beeton Aug 17 '16 at 14:57\braketdefined in this class by any chance?\braket{\vec{q'}|\vec{q}}would, I think, have the desired effect if the braket package were being used. – Dai Bowen Aug 17 '16 at 15:06