Context. IC 10 X-1 has recently been confirmed as a black hole (BH) + Wolf-Rayet (WR) X-ray binary, and NGC 300 X-1 is thought to be. The only other known BH+WR candidate is Cygnus X-3. IC 10 X-1 and NGC 300 X-1 have similar X-ray properties, with 0.3–10 keV luminosities ∼1038 erg s−1, and their X-ray lightcurves exhibit orbital periods ∼30 h. Aims. We investigate similarities between IC 10 X-1 and NGC 300 X-1, as well as differences between these systems and the known Galactic BH binary systems. Methods. We have examined all four XMM-Newton observations of NGC 300 X-1, as well as the single XMM-Newton observation of IC 10 X-1. For each observation, we extracted lightcurves and spectra from the pn, MOS1 and MOS2 cameras; power density spectra were constructed from the lightcurves, and the X-ray emission spectra were modeled. Results. Each source exhibits power density spectra that are well described by a power law with index, γ, ∼1. Such variability is characteristic of turbulence in wind accretion or disc-accreting X-ray binaries (XBs) in the high state. In this state, Galactic XBs with known BH primaries have soft, thermal emission; however the emission spectra of NGC 300 X-1 and IC 10 X-1 in the XMM-Newton observations are predominantly non-thermal. Furthermore, the Observation 1 spectrum of NGC 300 X-1 is strikingly similar to that of IC 10 X-1. Conclusions. The remarkable similarity between the behaviour of NGC 300 X-1 in Observation 1 and that of IC 10 X-1 lends strong evidence for NGC 300 X-1 being a BH+WR binary. Our spectral modeling rules out Bondi-Hoyle accretion onto a neutron star (NS) for NGC 300 X-1, but not a disc-accreting NS+WR system, nor a NS low mass X-ray binary (LMXB) that is merely coincident with the WR. We favour disc accretion for both systems, but cannot exclude Bondi-Hoyle accretion onto a BH. The unusual spectra of NGC 300 X-1 and IC 10 X-1 may be due to these systems existing in a persistently high state, whereas all known BH LMXBs are transient. The violent transition from low state to high state may temporarily eject the disc corona from the BH LMXBs, drastically reducing the non-thermal component. However, BH XBs in a persistent high state could retain their corona, and hence exhibit a large non-thermal component. LMC X-1 is a BH XB that has only been observed in the high state, and its spectrum is remarkably similar to those of NGC 300 X-1 in Observation 1 and IC 10 X-1. We therefore classify NGC 300 X-1, IC 10 X-1 and perhaps LMC X-1 as a new breed of BH XB, defined by their persistently high accretion rates and consequent stable disc configuration and corona. This scenario may also explain the lack of ultraluminous X-ray sources in the canonical soft state.