smaller than sign between underbraced expressions

This seems a decent positioning

documentclass{article}
usepackage{amsmath,amssymb}

DeclareMathOperator*{Ex}{mathbb{E}}

begin{document}

[
max_{w} U=
 underbrace{pi Ex_{theta_1} u (w'r)}_{S(theta_1)}
 underset{substack{vphantom{underbrace{scriptstylemathstrut}}<}}{+}
 underbrace{(1-pi)Ex_{theta_2} u (w'r)}_{S(theta_2)}
]

end{document}

Note the definition for Ex (use whatever name you like) that doesn't have the bad side effect of the E being lowered. Also note that the correct input is w', not w^{'}; don't use left and right in this case.