  Over the last two decades, motivations for modified gravity have emerged from
both theoretical and observational levels. $f(R)$ and Chern-Simons gravity have
received more attention as they are the simplest generalization. However,
$f(R)$ and Chern-Simons gravity contain only an additional scalar (spin-0)
degree of freedom and, as a result, do not include other modes of modified
theories of gravity. In contrast, quadratic gravity (also referred to as Stelle
gravity) is the most general second-order modification to 4-D general
relativity and contains a massive spin-2 mode that is not present in $f(R)$ and
Chern-Simons gravity. Using two different physical settings $-$ the
gravitational wave energy-flux measured by the detectors and the backreaction
of the emitted gravitational radiation on the spacetime of the remnant black
hole $-$ we demonstrate that massive spin-2 mode carries more energy than the
spin-0 mode. Our analysis shows that the effects are pronounced for
intermediate-mass black holes, which are prime targets for LISA.
