Blockchain technology has emerged as a transformative tool for secure data sharing across decentralised systems, particularly in finance, healthcare, and governance. However, despite its promise, the widespread adoption of blockchain platforms remains constrained by unresolved security threats and architecture-specific vulnerabilities. This paper presents a systematic literature review (SLR) that critically evaluates the security risks and countermeasures associated with blockchain-based data sharing models. The review focuses on three widely referenced platforms, Ethereum, Hyperledger Fabric, and MedRec, chosen for their relevance to public, permissioned, and healthcare-oriented blockchain deployments, respectively. The review analyzed 30 peer-reviewed publications from 2018 to 2025 sourced from IEEE Xplore, SpringerLink, ScienceDirect, and other digital libraries. Empirical insights from the reviewed literature indicate that Sybil attacks remain prevalent on public blockchains, although adaptive Proof-of-Stake protocols are reported to reduce their success rate considerably. Front-running and Miner Extractable Value–related behaviors are frequently observed in Ethereum-based decentralised finance ecosystems, often resulting in significant financial losses. Unauthorised access persists as a major concern, particularly for software wallets, which are commonly exposed to phishing and malware attacks. The findings underscore unique trade-offs across platforms: Ethereum supports transparency but is prone to transaction manipulation; Hyperledger ensures strong access control yet faces insider threat challenges; and MedRec enhances patient privacy but lacks robust mobile integration. This study provides a structured synthesis of existing threats, platform-level responses, and design trade-offs, offering guidance for stakeholders aiming to strengthen security in blockchain-based data-sharing infrastructures.