The need for executive control (EC) during bilingual language processing is thought to enhance these abilities, conferring a "bilingual advantage" on EC tasks. Recently, the reliability and robustness of the bilingual advantage has been questioned, with many variables reportedly affecting the size and presence of the bilingual advantage. This study investigates one further variable that may affect bilingual EC abilities: the similarity of a bilingual's two languages. We hypothesize that bilinguals whose two languages have a larger degree of orthographic overlap will require greater EC to manage their languages compared to bilinguals who use two languages with less overlap. We tested three groups of bilinguals with language pairs ranging from high- to low-similarity (German-English (GE), Polish-English (PE), and Arabic-English (AE), respectively) and a group of English monolinguals on a Stroop and Simon task. Two components of the bilingual advantage were investigated: an interference advantage, such that bilinguals have smaller interference effects than monolinguals; and a global RT advantage, such that bilinguals are faster overall than monolinguals. Between bilingual groups, these effects were expected to be modulated by script similarity. AE bilinguals showed the smallest Stroop interference effects, but the longest overall RTs in both tasks. These seemingly contradictory results are explained by the presence of cross-linguistic influences in the Stroop task. We conclude that similar-script bilinguals demonstrated more effective domain-general EC than different-script bilinguals, since high orthographic overlap creates more cross-linguistic activation and increases the daily demands on cognitive control. The role of individual variation is also discussed. These results suggest that script similarity is an important variable to consider in investigations of bilingual executive control abilities.