The use of wide-band-gap solid-state neutron detectors is expanding in environments where a compact size and high radiation hardness are needed, such as spallation neutron sources and next-generation fusion machines. Silicon carbide is a very promising material for use as a neutron detector in these fields because of its high resistance to radiation, fast response time, stability and good energy resolution. In this paper, measurements were performed with neutrons from the ISIS spallation source with two different silicon carbide detectors together with stability measurements performed in a laboratory under alpha-particle irradiation for one week. Some consideration to the impact of the casing of the detector on the detector’s counting rate is given. In addition, the detector response to Deuterium-Deuterium (D-D) fusion neutrons is described by comparing neutron measurements at the Frascati Neutron Generator with a GEANT4 simulation. The good stability measurements and the assessment of the detector response function indicate that such a detector can be used as both a neutron counter and spectrometer for 2–4 MeV neutrons. Furthermore, the absence of polarization effects during neutron and alpha irradiation makes silicon carbide an interesting alternative to diamond detectors for fast neutron detection.