adjustbox
comes with the option valign
. I chose valign=b
because I do not know what you are after, but you can change this of course.
\documentclass{article}
\usepackage{float}
\usepackage{subfig}
\usepackage{adjustbox}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes,positioning,shadows,trees,patterns}
\definecolor{blue}{HTML}{0081FF}
\definecolor{grey}{HTML}{B0B0B0}
\begin{document}
\begin{figure}[]
\centering
\subfloat[Oblivious Decision Tree]{
\adjustbox{max width=0.49\textwidth,valign=b}{
\begin{tikzpicture}[->,>=stealth',
level/.style={sibling distance = 5cm/#1, level distance = 2cm},
basic/.style={draw, text width=2cm, drop shadow, font=\sffamily, rectangle},
split/.style={basic, rounded corners=2pt, thin, align=center, fill=grey},
leaf/.style={basic, rounded corners=6pt, thin,align=center, fill=blue, text width=1cm}]
\node [split] {$x_1<0.75$}
child{ node [split] {$x_2<1.25$}
child{ node [leaf] {$\omega_{00}$} edge from parent node[above left] {$no$}}
child{ node [leaf] {$\omega_{01}$} edge from parent node[above right] {$yes$}}
edge from parent node[above left] {$no$}}
child{ node [split] {$x_2<1.25$}
child{ node [leaf] {$\omega_{10}$} edge from parent node[above left] {$no$}}
child{ node [leaf] {$\omega_{11}$} edge from parent node[above right] {$yes$}}
edge from parent node[above right] {$yes$}
};
\end{tikzpicture}
}
}~\subfloat[Oblivious Decision Tree]{
\adjustbox{valign=b}{\begin{tabular}{llll}
\hline
\(x_1<0.75\) & \(x_2<1.25\) & q & w \\
\hline
false & false & 00b & \( w_{00} \) \\
false & true & 01b & \( w_{01} \) \\
true & false & 10b & \( w_{10} \) \\
true & true & 11b & \( w_{11} \) \\
\hline
\end{tabular}}
}
\caption{}
\label{fig:decision-tree}
\end{figure}
\end{document}

The advantage of this is that you can load and align the same tikzpicture
in different ways without modifying it.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents*}{mypic.tex}
\begin{tikzpicture}[->,>=stealth',
level/.style={sibling distance = 5cm/#1, level distance = 2cm},
basic/.style={draw, text width=2cm, drop shadow, font=\sffamily, rectangle},
split/.style={basic, rounded corners=2pt, thin, align=center, fill=grey},
leaf/.style={basic, rounded corners=6pt, thin,align=center, fill=blue, text width=1cm}]
\node [split] {$x_1<0.75$}
child{ node [split] {$x_2<1.25$}
child{ node [leaf] {$\omega_{00}$} edge from parent node[above left] {$no$}}
child{ node [leaf] {$\omega_{01}$} edge from parent node[above right] {$yes$}}
edge from parent node[above left] {$no$}}
child{ node [split] {$x_2<1.25$}
child{ node [leaf] {$\omega_{10}$} edge from parent node[above left] {$no$}}
child{ node [leaf] {$\omega_{11}$} edge from parent node[above right] {$yes$}}
edge from parent node[above right] {$yes$}
};
\end{tikzpicture}
\end{filecontents*}
\usepackage{float}
\usepackage{subfig}
\usepackage{adjustbox}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes,positioning,shadows,trees,patterns}
\definecolor{blue}{HTML}{0081FF}
\definecolor{grey}{HTML}{B0B0B0}
\begin{document}
\begin{figure}[]
\centering
\subfloat[Oblivious Decision Tree]{
\adjustbox{max width=0.49\textwidth,valign=b}{\input{mypic.tex}}
}~\subfloat[Oblivious Decision Tree]{
\adjustbox{valign=b}{\begin{tabular}{llll}
\hline
\(x_1<0.75\) & \(x_2<1.25\) & q & w \\
\hline
false & false & 00b & \( w_{00} \) \\
false & true & 01b & \( w_{01} \) \\
true & false & 10b & \( w_{10} \) \\
true & true & 11b & \( w_{11} \) \\
\hline
\end{tabular}}
}
\caption{}
\label{fig:decision-tree}
\end{figure}
\end{document}
The above was under the assumption that you want to have the freedom to choose the alignment. If you are sure that you want to align at the bottom, you can do as John Kormylo pointed out, only align the tabular. This variation is on something else, namely that you can produce the tree much more conveniently with forest
. It allows you to do everything automatically.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents*}{myforest.tex}
\begin{forest}
for tree={l sep=2em,draw,blur shadow,font=\sffamily, rectangle,thin,align=center,
where n children=0{rounded corners=6pt,fill=myblue}{rounded corners=2pt,
fill=mygrey},
where n=1{edge label={node[above left,pos=0.9,font=\sffamily\small]{yes}}}{%
edge label={node[above right,pos=0.9,font=\sffamily\small]{no}}},
edge={-stealth}}
[$x_1<0.75$
[$x_2<1.25$
[$\omega_{00}$]
[$\omega_{01}$]
]
[$x_2<1.25$
[$\omega_{00}$]
[$\omega_{01}$]
]
]
\end{forest}
\end{filecontents*}
\usepackage{float}
\usepackage{subfig}
\usepackage{forest}
\usetikzlibrary{shadows.blur}
\definecolor{myblue}{HTML}{0081FF}
\definecolor{mygrey}{HTML}{B0B0B0}
\begin{document}
\begin{figure}[]
\centering
\subfloat[Oblivious Decision Tree]{\input{myforest.tex}%
}\qquad\subfloat[Oblivious Decision Tree]{\begin{tabular}[b]{llll} % John Kormylo
\hline
\(x_1<0.75\) & \(x_2<1.25\) & q & w \\
\hline
false & false & 00b & \( w_{00} \) \\
false & true & 01b & \( w_{01} \) \\
true & false & 10b & \( w_{10} \) \\
true & true & 11b & \( w_{11} \) \\
\hline
\end{tabular}}
\caption{}
\label{fig:decision-tree}
\end{figure}
\end{document}
