You can add a scale to each node. Here is a version with and with the default of scale=1 and scale=1.3 appliled:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{shapes.misc}
\begin{document}
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1] (reg) {Regular node};
\end{tikzpicture}
%
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1.3] (reg) {Regular node};
\end{tikzpicture}
\end{document}
If you have an issue with adding multiple lines of text to the node then you need to specify the width of the text and an alignment with:
text width=2.4cm,align=center
This is independent of the scaling issue and yields:

\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{shapes.misc}
\begin{document}
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1,text width=2.4cm,align=center] (reg) {Enlarged node with many lines that flow down};
\end{tikzpicture}
%
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1.3,text width=2.4cm,align=center] (reg) {Enlarged node with many lines that flow down};
\end{tikzpicture}
\end{document}
If you prefer to manually decide where the line break should be, by adding a \\, then you do not need to specify text width=2.4cm. So use:
\node ... {Enlarged node \\ with many lines \\ that flow down}
Here is the full code for this:
\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{shapes.misc}
\begin{document}
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1,text width=2.4cm,align=center] (reg) {Enlarged node \\ with many lines \\ that flow down};
\end{tikzpicture}
%
\begin{tikzpicture}[node distance=1.5cm]
\node[regular polygon, regular polygon sides=6, shape aspect=0.5, minimum width=4cm, minimum height=1cm, draw,scale=1.3,align=center] (reg) {Enlarged node \\ with many lines \\ that flow down};
\end{tikzpicture}
\end{document}