Vertical alignment of "nobeforeafter" tcolorbox

Two options; the first one uses a manual adjustment made using the baseline key for the tcolorboxes, and the second one uses the option valign=c for an \adjustbox from the adjustbox package; the setting is done automatically using before and after:

\newtcbox{\LittleBox}[1][]{
  enhanced,
  before=\adjustbox{valign=c}\bgroup,
  after=\egroup,#1
}

The complete code with both possibilities:

\documentclass[]{article}
\usepackage[skins]{tcolorbox}
\usepackage{adjustbox}

\newtcolorbox{mybox}[1][]{
  enhanced,
  sidebyside,
  sidebyside align= center,   
  colbacktitle=white,
  coltitle=black,
  colback=white,
  fonttitle=\large\bfseries,
  #1
}
\newtcbox{\LittleBox}[1][]{
  enhanced,
  before=\adjustbox{valign=c}\bgroup,
  after=\egroup,#1
}
\newtcbox{\LittleBoxA}[1][]{
  enhanced,
  nobeforeafter,#1
}

\begin{document}

\begin{mybox}[title= Little boxes centered vertically]
\LittleBoxA[baseline=-1ex]{\scriptsize First} 
\LittleBoxA{\huge Second}
\tcblower
\LittleBoxA{\Large Third}
\LittleBoxA[baseline=-0.5ex]{\small Fourth}
\end{mybox}

\begin{mybox}[title= Little boxes centered vertically]
\LittleBox{\scriptsize First} 
\LittleBox{\huge Second}
\tcblower
\LittleBox{\Large Third}
\LittleBox{\small Fourth}
\end{mybox}

\end{document}

tcolorbox in version published in 2014-10-10 introduced box align option which solves this problem.

Default value for box align is bottom, but it's possible to also choose top, center and base. Therefore, a little change to LittleBox will do the work

\newtcbox{\LittleBox}[1][]{enhanced, nobeforeafter, box align = center, #1}

\documentclass[]{article}
\usepackage[skins]{tcolorbox}

\begin{document}

\newtcbox{\LittleBox}[1][]{enhanced, nobeforeafter, box align = center, #1}%

\begin{tcolorbox}[enhanced, sidebyside, sidebyside align= center, 
    colbacktitle=white, coltitle=black, colback=white, 
    fonttitle=\large\bfseries, title= Little boxes centered vertically]

\LittleBox{\scriptsize First} 
\LittleBox{\huge Second}
\tcblower
\LittleBox{\Large Third}
\LittleBox{\small Fourth}

\end{tcolorbox}

\end{document}