The boxing interferes with the math spacing, if you make the phantoms visible you see what is being braced:
If you correct for the mathop spacing you can make them align exactly:

\documentclass[border=12pt]{article}
\usepackage{amsmath,color}
\begin{document}
$
\lefteqn{\textstyle\overbrace{\phantom{1+2+3+4}}^{\alpha}}1+2+
\underbrace{3+4+
\lefteqn{\textstyle\overbrace{\phantom{5+6+7}}^{\beta}}5+6}_{\gamma}+7
$
\def\xphantom#1{\hbox{{\color{red}$#1$}}}
$
\lefteqn{\textstyle\overbrace{\xphantom{1+2+3+4}}^{\alpha}}1+2+
\underbrace{3+4+
\lefteqn{\textstyle\overbrace{\xphantom{5+6+7}}^{\beta}}5+6}_{\gamma}+7
$
$\setbox0\hbox{$3+4$}
\overbrace{1+2+3+4}^{\alpha}
\kern-\wd0\!
\underbrace{3+4+5+6}_{\gamma}
\kern-\wd0\!
\overbrace{5+6+7}^{\beta}
$
\end{document}
See the discussion in
How to fix the math-spacing when a lot of \phantom, \mathrlap, etc. are used?