Boldness (i.e., the propensity to take risks) and exploratory behaviours can influence an animal’s ability to acquire resources, thus affecting competitive success. The Asian shore crab, Hemigrapsus sanguineus, and European green crab, Carcinus maenas, co-occur as highly invasive species in coastal areas of the United States, and more recently, in Atlantic Canada. Both crabs use structurally complex rocky intertidal habitat and consume similar macroalgal and invertebrate prey, such that they likely compete for resources. Competitive interactions between co-invaders could influence the success of either species, affecting their impacts on the ecosystem. Yet, there is a gap in research comparing behaviours, such as boldness or exploration, between co-invaders such as these crabs. Here, the boldness of H. sanguineus and C. maenas are compared by investigating their tendencies to exit preferred rocky habitat with shelter to explore an open and brightly lit area. The crabs’ exploratory tendencies are also compared, by evaluating if the species spontaneously alternate (i.e., preferentially explore regions that they have least recently explored), an indicator of efficient exploration. The two species had similar latencies when exiting the sheltered habitat, but C. maenas spent more time in the open area overall. Both crabs also tended to spontaneously alternate, but H. sanguineus had a greater tendency to do so than C. maenas, revealing for the first time the existence of significant differences in spontaneous alternation behaviour between invasive species. If the strong exploration ability of H. sanguineus can improve the species’ ability to find resources, it may have a competitive advantage over C. maenas in regions where the crabs co-occur.