The rapid expansion of cyberspace has greatly facilitated the strategic shift of traditional crimes to online platforms. This has included malicious actors, such as extremist organisations, making use of online networks to disseminate propaganda and incite violence through radicalising individuals. In this article, we seek to advance current research by exploring how supporters of extremist organisations craft and disseminate their content, and how posts from counter-extremism agencies compare to them. In particular, this study will apply computational techniques to analyse the narratives of various pro-extremist and counter-extremist Twitter accounts, and investigate how the psychological motivation behind the messages compares between pro-ISIS and counter-extremism narratives. Our findings show that pro-extremist accounts often use different strategies to disseminate content (such as the types of hashtags used) when compared to counter-extremist accounts across different types of organisations, including accounts of governments and NGOs. Through this study, we provide unique insights into both extremist and counter-extremist narratives on social media platforms. Furthermore, we define several avenues for discussion regarding the extent to which counter-messaging may be effective at diminishing the online influence of extremist and other criminal organisations.