Font size in \pmatrix: Elegant Summation in big Vectors

Use always \dfrac and \limits:

\documentclass{book}
\usepackage{amsmath}

\begin{document}
\begin{equation}
    \begin{pmatrix}
        \sum\limits_{j=1}^{q_{k}} \dfrac{\vec{e}_{k,j}}{b_{k,j} -  \vec{m}_{k,j}^T \vec{x}_{k} - 
        \vec{e}_{k,j}^T 
        \vec{u}_{k}} \\
        \sum\limits_{j=1}^{q_{k+1}} \dfrac{\begin{pmatrix} \vec{e}_{k+1,j} & \vec{m}_{k+1,j} 
        \end{pmatrix}^T}{b_{k+1,j} -  \vec{e}_{k+1,j}^T \vec{u}_{k+1} -  \vec{m}_{k+1,j}^T \vec{x}_{k+1}} \\
        \vdots \\
        \sum\limits_{j=1}^{q_{k+N-1}} \dfrac{\begin{pmatrix} \vec{e}_{k+N-1,j} & \vec{m}_{k+N-1,j} 
        \end{pmatrix}^T}{b_{k+N-1,j} -  \vec{e}_{k+N-1,j}^T \vec{u}_{k+N-1} -  \vec{m}_{k+N-1,j}^T 
        \vec{x}_{k+N-1}} \\
        \sum\limits_{j=1}^{q_{k+N}} \dfrac{\vec{m}_{k+N,j}}{b_{k+N,j} -  \vec{m}_{k+N,j}^T \vec{x}_{k+N}}
\end{pmatrix}
\end{equation}

\end{document}

I propose another layout, with medium-sized fractions from nccmath and an alignment of the sum symbols, thanks to the pmatrix* environment from mathtools and package eqparbox:

\documentclass{book}
\usepackage{mathtools, nccmath}
\usepackage{bm}
\usepackage{eqparbox, booktabs}
\newcommand{\eqmathbox}[2][M]{\eqmakebox[#1]{$\scriptstyle#2$}}
\newcommand{\msum}{\medop\sum\limits}
%
\begin{document}

\begin{equation}
 \begin{pmatrix*}[l]
 \msum_{j=1}^{\eqmathbox{q_{k}}} \mkern-12mu \frac{\bm{e}_{k,j}}{b_{k,j} - \bm{m}_{k,j}^T \bm{x}_{k} - \bm{e}_{k,j}^T \bm{u}_{k}} \\ \addlinespace
\msum_{j=1}^{\eqmathbox{q_{k+1}}} \mkern-12mu \frac{\bigl(\bm{e}_{k+1,j} \enspace \bm{m}_{k+1,j}\bigr)^T}{b_{k+1,j} - \bm{e}_{k+1,j}^T \bm{u}_{k+1} - \bm{m}_{k+1,j}^T \bm{x}_{k+1}} \\
\eqmathbox{ ⋮ } \\[0.5ex]
        \msum_{j=1}^{\eqmathbox{q_{k+N-1}}}\mkern-12mu \mfrac{\bigr( \bm{e}_{k+N-1,j} \quad \bm{m}_{k+N-1,j} \bigr)^T}{b_{k+N-1,j} - \bm{e}_{k+N-1,j}^T
 \bm{u}_{k+N-1} - \bm{m}_{k+N-1,j}^T \bm{x}_{k+N-1}} \\ \addlinespace
 \msum_{j=1}^{\eqmathbox{q_{k+N}}}\mkern-12mu \frac{\bm{m}_{k+N,j}}{b_{k+N,j} - \bm{m}_{k+N,j}^T \bm{x}_{k+N}}
\end{pmatrix*}
\end{equation}

\end{document} 

I've seen that the main problem is that you are using pmatrix environment inside another pmatrix environment. That's causing the differences in sizes between the numerator and denominator.

One solution, if you don't fully understand the code that you have with the pmatrix, is to use plain arrays. You can create an array of one column, and every entry in that array is one summation. If you want more space, add a blank line or create a new line. This is the code:

\documentclass{book}
\usepackage{amsmath}

\begin{document}

\[  % begin math environment
\left(  % left parenthesis
\begin{array}{c}  % begins an array of one column

\sum_{j=1}^{q_{k}} \frac{\vec{e}_{k,j}}{b_{k,j}-\vec{m}_{k,j}^\vec{x}_{k}-\vec{e}_{k,j}^T \vec{u}_{k}} \\ % some space
\\ % more space
\sum_{j=1}^{q_{k+1}} \frac{\left(\vec{e}_{k+1,j}~\vec{m}_{k+1,j}\right)^T}{b_{k+1,j}-\vec{e}_{k+1,j}^T \vec{u}_{k+1}-\vec{m}_{k+1,j}^T\vec{x}_{k+1}} \\ % some space
\\ % more space       
\vdots \\ % some space
\\ % more space
\sum_{j=1}^{q_{k+N-1}}\frac{\left(\vec{e}_{k+N-1,j}~\vec{m}_{k+N-1,j}\right)^T}{b_{k+N-1,j}-\vec{e}_{k+N-1,j}^T\vec{u}_{k+N-1}-\vec{m}_{k+N-1,j}^T \vec{x}_{k+N-1}} \\ % some space
\\ % more space 
\sum_{j=1}^{q_{k+N}}\frac{\vec{m}_{k+N,j}}{b_{k+N,j}-\vec{m}_{k+N,j}^T\vec{x}_{k+N}}

\end{array}  % ends array
\right)  % right hand side parenthesis
\] % ends math environment

\end{document}

Another solution would be to not use pmatrix environments in the summations. Just use \left( \right) for the big parenthesis, like this:

\documentclass{book}
\usepackage{amsmath}

\begin{document}

\[  % begin math environment
\begin{pmatrix}

\sum_{j=1}^{q_{k}} \frac{\vec{e}_{k,j}}{b_{k,j}-\vec{m}_{k,j}^\vec{x}_{k}-\vec{e}_{k,j}^T \vec{u}_{k}} \\ % some space
\\ % more space
\sum_{j=1}^{q_{k+1}} \frac{\left(\vec{e}_{k+1,j}~\vec{m}_{k+1,j}\right)^T}{b_{k+1,j}-\vec{e}_{k+1,j}^T \vec{u}_{k+1}-\vec{m}_{k+1,j}^T\vec{x}_{k+1}} \\ % some space
\\ % more space       
\vdots \\ % some space
\\ % more space
\sum_{j=1}^{q_{k+N-1}}\frac{\left(\vec{e}_{k+N-1,j}~\vec{m}_{k+N-1,j}\right)^T}{b_{k+N-1,j}-\vec{e}_{k+N-1,j}^T\vec{u}_{k+N-1}-\vec{m}_{k+N-1,j}^T~\vec{x}_{k+N-1}} \\ % some space
\\ % more space 
\sum_{j=1}^{q_{k+N}}\frac{\vec{m}_{k+N,j}}{b_{k+N,j}-\vec{m}_{k+N,j}^T\vec{x}_{k+N}}

\end{pmatrix}
\] % ends math environment

\end{document}