  We systematically compare the temporal and spectral properties of 53
Supernova (SN)-associated and 15 Kilonova (KN)-associated Gamma-Ray Bursts
(GRBs). We find that the spectral parameters of both types GRBs are identically
and lognormally distributed, consistent with those normal GRBs. The bolometric
luminosities of SN/GRBs and KN/GRBs have a triple form with the corresponding
break luminosities of SN/GRBs are roughly two orders of magnitude larger than
those of KN/GRBs. We build the power-law relations between the spectral lag and
the luminosity of prompt $\gamma$-rays with indices of $-1.43\pm0.33$ for
SN/GRBs and $-2.17\pm0.57$ for KN/GRBs in the laboratory frame, which are
respectively coincident with the rest-frame values. We verify that both SN/GRBs
and KN/GRBs comply with their own Amati relations that match those of long and
short GRBs, respectively. Analyzing X-ray afterglows with good plateau
segments, we build the power-law relations between the X-ray luminosity and the
plateau time with an index of $-1.12\pm0.17$ for KN/GRBs and $-1.08\pm0.22$ for
SN/GRBs, which can be well explained by the relativistic shock driven by an
energy injection. The plots of luminosity-lag, Amati relation and
luminosity-time show heavy overlap between the two types of GRBs, implying that
they might share the same radiation mechanism despite originating from
different progenitors or central engines.
