The following example shows that multicols treats pagebreaks as separate orderings.
\documentclass{article}
\usepackage[margin=0.5in]{geometry}\geometry{a4paper}
\usepackage{multicol,tikz}
\scrollmode
\begin{document}
\newcommand{\drawrect}[1]{\begin{tikzpicture} \draw (-1.5,-1.5) rectangle (1.5,1.5); \node at (0,0) {#1}; \end{tikzpicture}}
\begin{multicols}{3}\raggedright
\drawrect{1}
\drawrect{2}
\drawrect{3}
\drawrect{4}
\drawrect{5}
\drawrect{6}
\drawrect{7}
\drawrect{8}
\drawrect{9}
\drawrect{10}
\drawrect{11}
\drawrect{12}
\end{multicols}
\renewcommand{\drawrect}[1]{\begin{tikzpicture} \draw (-2.5,-3.5) rectangle (2.5,3.5); \node at (0,0) {#1}; \end{tikzpicture}}
\begin{multicols}{3}\raggedright
\drawrect{1}
\drawrect{2}
\drawrect{3}
\drawrect{4}
\drawrect{5}
\drawrect{6}
\drawrect{7}
\drawrect{8}
\drawrect{9}
\drawrect{10}
\drawrect{11}
\drawrect{12}
\end{multicols}
\end{document}
I want the 2nd ordering to be exactly like the first.
Example using parcolumns:
\documentclass{article}
\usepackage[margin=0.5in]{geometry}\geometry{a4paper}
\usepackage{multicol,tikz}
\usepackage{parcolumns}
\scrollmode
\begin{document}
\newcommand{\drawrect}[1]{\begin{tikzpicture} \draw (-1.5,-1.5) rectangle (1.5,1.5); \node at (0,0) {#1}; \end{tikzpicture}}
\begin{parcolumns}[nofirstindent]{3}
\colchunk{
\drawrect{1}
\drawrect{2}
\drawrect{3}
\drawrect{4}}
\colchunk{
\drawrect{5}
\drawrect{6}
\drawrect{7}
\drawrect{8}}
\colchunk{
\drawrect{9}
\drawrect{10}
\drawrect{11}
\drawrect{12}}
\end{parcolumns}
\renewcommand{\drawrect}[1]{\begin{tikzpicture} \draw (-2.5,-3.5) rectangle (2.5,3.5); \node at (0,0) {#1}; \end{tikzpicture}}
\begin{parcolumns}[nofirstindent]{3}
\colchunk{
\drawrect{1}
\drawrect{2}
\drawrect{3}
\drawrect{4}}
\colchunk{
\drawrect{5}
\drawrect{6}
\drawrect{7}
\drawrect{8}}
\colchunk{
\drawrect{9}
\drawrect{10}
\drawrect{11}
\drawrect{12}}
\end{parcolumns}
\end{document}

parcolumnspackage then, although your code would have to manually distinguish between the columns. That is, the process is not as well-automated as inmulticol. – Werner May 9 '12 at 20:24