\documentclass[a4paper]{article}
\usepackage[greek,english,provide=*]{babel}    % Babel's Greek "ini"
\newcommand{\langGreek}{\foreignlanguage{greek}}

\usepackage{fontspec}
\setmainfont{FreeSerif}
% \setmainfont{DejaVu Serif}
% \setmainfont{Droid Sans}
% \setmainfont{Linux Libertine O}
% \setmainfont{Liberation Serif}
% \setmainfont{cmunrm.otf}

\begin{document}


U+1FEF GREEK VARIA and U+1FFD GREEK OXIA

English:  ` ´ → \MakeUppercase{` ´}

Greek: \langGreek{` ´ → \MakeUppercase{` ´}}


U+0060 GRAVE ACCENT and U+00B4 ACUTE ACCENT

English:  ` ´ → \MakeUppercase{` ´}

Greek: \langGreek{` ´ → \MakeUppercase{` ´}}


\end{document}


* Spacing U+1FEF GREEK VARIA becomes U+2018 LEFT SINGLE QUOTATION MARK
  (visible difference with XeTeX and DejaVu),

With old MakeUppercase: Spacing accents: ῀ ` ´ ῾ ᾽ ᾿ → ῀ ` ´ ῾ ᾽ ᾿

With new MakeUppercase: Spacing accents: ῀ ` ´ ῾ ᾽ ᾿ → ῀ ‘ ´ ῾ ᾽ ᾿

U+0060 GRAVE ACCENT and U+00B4 ACUTE ACCENT
English: ‘ ´ → ‘ ´
