Traditional niche theory predicts that when species compete for one limiting resource in simple ecological settings the more fit competitor should exclude the less fit competitor. Since the advent of neutral theory ecologists have increasingly become interested both in how the magnitude of fitness inequality between competitors and stochasticity may affect this prediction. We used numerical simulations to investigate the outcome of two-species resource competition along gradients of fitness inequality (inequality in R*) and initial population size in the presence of demographic stochasticity. We found that the deterministic prediction of more fit competitors excluding less fit competitors was often unobserved when fitness inequalities were low or stochasticity was strong, and unexpected outcomes such as dominance by the less fit competitor, long-term co-persistence of both competitors or the extinction of both competitors could be common. By examining the interaction between fitness inequality and stochasticity our results mark the range of parameter space in which the predictions of niche theory break down most severely, and suggest that questions about whether competitive dynamics are driven by neutral or niche processes may be locally contingent.