  This article is devoted to the comparative study of the effects of the
Lorentz symmetry violation (LV) arising in Kalb-Ramond (KR) and Bumblebee (BM)
field models. We study optical appearance with accretion, Quasinormal modes,
ringdown waveforms, Hawking radiation, and weak gravitational lensing. The
horizon radius, photon radius, and the critical impact parameter for KR BHs
decrease with the LV parameter $\a$. In contrast, they remain independent of
the BM parameter $\b$ and have values the same as those for \s BH. We find that
a KR BH is brighter than a \s or BM BH for static and infalling accretion. The
BM BH, on the other hand, is brighter than a \s BH when the accretion is static
but becomes darker for an infalling accretion. Our investigation into
quasinormal modes (QNMs) and ringdown waveforms provides deeper insight into
the difference in observational imprints of LV parameters. It reveals that GWs
emitted by KR BHs have larger frequencies and decay faster than those emitted
by \s or BM BHs for scalar and electromagnetic perturbations. We then study the
greybody factor (GF) and power emitted for both BHs. The Hawking temperature is
higher for a KR BM and lower for a BM BH than a \s BH. It also reveals that the
transmission probability decreases with $\a$ and $\b$. A comparison of GFs for
KR and BM BHs reveals that the transmission probability is higher for BM BH. We
also study the effect of LV on the power emitted in the form of Hawking
radiation. Power received by an asymptotic observer is larger for a KR BH. We
obtain higher-order corrections in the deflection angle and graphically
illustrate the impact of $\a$ and $\b$. We observe that a light ray gets
deflected most from its path when passing by a \s BH, and the deflection is
least when it passes by a KR BH. Our study conclusively shows that we can
differentiate between KR and BM BHs based on astrophysical observations.
