[ABRIDGED] IC10 X-1 has recently been confirmed as a black hole (BH) + Wolf-Rayet (WR) X-ray binary, and NGC300 X-1 is thought to be. IC10 X-1 and NGC300 X-1 have similar X-ray properties, with luminosities ~10^38 erg/s, and orbital periods ~30 hr. We investigate similarities between these two, as well as differences between them and the known Galactic BH binary systems. We have examined XMM-Newton observations of NGC300 X-1 and IC10 X-1. We extracted lightcurves and spectra; power density spectra (PDS) were constructed from the lightcurves, and the X-ray emission spectra were modeled. Each source exhibits PDS that are characteristic of 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 our targets are predominantly non-thermal. Furthermore, the Observation 1 spectrum of NGC300 X-1 is strikingly similar to that of IC10 X-1. The remarkable similarity between the behaviour of NGC300 X-1 in Observation 1 and that of IC10 X-1 lends strong evidence for NGC300 X-1 being a (BH+WR) binary. The unusual spectra of NGC300 X-1 and IC10 X-1 may be due to these systems existing in a persistently high state, whereas all known BH LMXBs are transient. 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 our targets. We therefore classify NGC300 X-1, IC10 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.
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