The advent of the Internet of Things (IoT) technology and the term “connect everything to everything” bring up a new standard for IPv6 over Low-power Wireless Personal Area Networks (6LoWPAN), which are used in many applications. Authentication mechanisms between 6LoWPAN-based constrained devices are an important criterion for establishing secure connections against potential attacks, regardless of the size and capabilities of these devices. Therefore, developing authentication protocols that match the capabilities of 6LoWPAN devices is urgently needed. There is a conspicuous gap in the comprehensive 6LoWPAN Authentication and Key Agreement protocols (AKA) survey, encompassing End-to-End and Machine-to-Machine authentication paradigms. This study provides an innovative perspective that distinguishes it from existing authentication studies to fill this gap and comprehensively analyze AKA-based 6LoWPAN protocols to shed light on the field. A comprehensive survey of AKA protocols for 6LoWPAN examined their suitability within wireless sensor networks and the broader IoT context. This comparative assessment is based on critical factors such as lightweight cryptography solutions, threats, countermeasures, formal and informal security verification techniques and operating systems, and simulations. Additionally, a framework is introduced to facilitate the design of AKA protocols to provide a foundation for new researchers in the field while highlighting key open issues and proposing future research endeavors. Our survey aims to provide benchmark references to help researchers and application developers conduct further research.