Small matrix spacing and sizing

I wouldn't auto-size the parentheses; instead, I'd apply \bigl and \bigr to both smallmatrix environments. If you insist on auto-sizing, I'd go with the psmallmatrix environment (provided by the mathtools package) and save myself some keystrokes.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
setting 
$\bigl(\begin{smallmatrix}
\beta_x \\ \beta_y
\end{smallmatrix}\bigr) = 
\bigl(\begin{smallmatrix}
0.01 \\ 0
\end{smallmatrix}\bigr)$ 
results in a \dots

\medskip
setting 
$\begin{psmallmatrix}
\beta_x \\ \beta_y
\end{psmallmatrix} = 
\begin{psmallmatrix}
0.01 \\ 0
\end{psmallmatrix}$ 
results in a \dots
\end{document}

You can load mathtools and use the simple syntax:

setting $\begin{psmallmatrix}
\beta_x \\
\beta_y
\end{psmallmatrix} = \begin{psmallmatrix}
0.01\mathstrut \\
0
\end{psmallmatrix}$ results in a ...

Use a \vphantom.

And as MadyYuvi correctly suggests, additional control can be gained at limiting the vertical height of the parens by replacing the \left...\right nomenclature with \bigl...\bigr

\documentclass{article}
\usepackage{mathtools}
\begin{document}
setting $\bigl(\begin{smallmatrix}
\beta_x \\
\beta_y
\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix}
0.01\vphantom{\beta_x} \\
0\vphantom{\beta_y}
\end{smallmatrix}\bigr)$ results in a ...
\end{document}