I am using the following MWE. First time with unicode-math, second time without it:
% arara: lualatex
\documentclass{article}
\usepackage{amssymb}
%\usepackage{unicode-math}
\begin{document}
$\tilde\Box \hat\Box \bar\Box$
\end{document}


Where does the difference come from? The kerning is clearly broken.
amssymb.sty 2013/01/14 v3.01 AMS font symbols
unicode-math.sty 2013/05/21 v0.7e Unicode mathematics support for XeTeX and LuaTeX
Edit
Barbara Beeton suggested to try the package latexsym instead of amssymb. This results in worse vertical positioning and the very same effect for I/O unicode-math:
% arara: lualatex
\documentclass{article}
\usepackage{latexsym}
%\usepackage{unicode-math}
\begin{document}
$\tilde\Box \hat\Box \bar\Box$
\end{document}



latexsymalso defines\Box. what happens when you use that one instead ofamssymb? – barbara beeton May 07 '14 at 17:27