Why does a columnbreak between equation environments insert vertical space?

Inserting an empty line in-front of the columnbreak makes it look the same.

You can set, locally, multicolsep to 0pt. However, it would be simpler to use tabularx: I propose to define a newcolumn type with cells contents automatically in the equation environment, making the typing very simple:

documentclass{article}
usepackage{lipsum}
usepackage{multicol}
usepackage{nccmath}
usepackage{tabularx}
makeatletter
newcommand*{compress}{@minipagetrue}
makeatother

newcolumntype{E}{@{}>{compressequation}X<{endequation}@{}}

begin{document}
lipsum[11]
  setlength{columnseprule}{0.4pt}
 {setlength{multicolsep}{0pt}
    begin{multicols}{2}
        begin{equation} a = a end{equation}
        columnbreak % why does this columnbreak insert vspace?
        begin{equation} a = a end{equation}
    end{multicols}
    begin{multicols}{2}
        begin{equation} a = a end{equation}
        begin{equation} a = a end{equation}
    end{multicols}
}
vspace{4ex}

   {centeringbelowdisplayskip=0pt
    begin{tabularx}{textwidth}{@{}E@{enspace}|@{enspace}E@{}}
    a = a & a = a [-1ex]
     a = a & a = a
    end{tabularx}
}
end{document}