Why are different versions of "theta" used, here?

Question

If you compile the following code, you'll realize that, in the first case, the Greek letter theta is open, whereas, in the second one, it is close.

This happens only with some Greek fonts: Didot, Artemisia; not with lgr and others.

Why are different versions of theta used, here? Is there a way to control them (as with XeLaTeX?)

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek.polutoniko,italian]{babel}
\newcommand{\GR}[1]{%
  {\fontfamily{udidot}\selectfont\foreignlanguage{greek}{#1}}%
}
\begin{document}
\GR{j'esis >al'hjeia}
\end{document}

Answer 1

It's a precise choice of the font designers. The .vf file in this case is gdidotrg6a.vf and running

vftovp gdidotrg6a.vf

shows

(BOUNDARYCHAR O 1)
(LIGTABLE
   (LABEL BOUNDARYCHAR)
   (LIG C j O 14)
   (STOP)

This means that the boundary chararacter is enabled for this font and, when j follows the boundary character, which is implicitly present at the start of a word, it is substituted by the glyph at position octal 14. The font table shows it's an open theta

If you want the closed theta also in the initial position, you need to use \noboundary before it.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek.polutoniko,italian]{babel}
\newcommand{\GR}[1]{%
  {\fontfamily{udidot}\selectfont\foreignlanguage{greek}{#1}}%
}
\begin{document}
\GR{\noboundary j'esis >al'hjeia}
\end{document}

If you want the open theta throughout, the only way is to input it as ^^L (after changing its status).

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek.polutoniko,italian]{babel}

\catcode`\^^L=11

\newcommand{\GR}[1]{%
  {\fontfamily{udidot}\selectfont\foreignlanguage{greek}{#1}}%
}
\begin{document}
\GR{j'esis >al'h^^Leia}
\end{document}

The j at the left word boundary need not be typed as ^^L.

There's no way to act on this from the TeX side, because it's a font property.