  We present a comprehensive study of an unbiased sample of 150 nearby (<z> =
0.014) core-collapse supernova (CCSN) host galaxies drawn from the All-Sky
Automated Survey for Supernovae (ASAS-SN) for direct comparison to the nearest
LGRB and SLSN hosts. We use public imaging surveys to gather multi-wavelength
photometry for all CCSN host galaxies and fit their spectral energy
distributions (SEDs) to derive stellar masses and integrated star formation
rates. CCSNe populate galaxies across a wide range of stellar masses, from blue
and compact dwarf galaxies to large spiral galaxies. We find 33(+4,-4) per cent
of CCSNe are in dwarf galaxies (M < 10^9 M_Sun) and 2(+2,-1) per cent are in
dwarf starburst galaxies (sSFR > 10^-8 yr^-1). We reanalyse low-redshift SLSN
and LGRB hosts from the literature (out to $z<0.3$) in a homogeneous way and
compare against the CCSN host sample. The relative SLSN to CCSN supernova rate
is increased in low-mass galaxies and at high specific star-formation rates.
These parameters are strongly covariant and we cannot break the degeneracy
between them with our current sample, although there is some evidence that both
factors may play a role. Larger unbiased samples of CCSNe from projects such as
ZTF and LSST will be needed to determine whether host-galaxy mass (a proxy for
metallicity) or specific star-formation rate (a proxy for star-formation
intensity and potential IMF variation) is more fundamental in driving the
preference for SLSNe and LGRBs in unusual galaxy environments.
