The Internet of Things (IoT) is the next big challenge for the research community where the IPv6 over low power wireless personal area network (6LoWPAN) protocol stack is a key part of the IoT. Recently, the IETF ROLL and 6LoWPAN working groups have developed new IP based protocols for 6LoWPAN networks to alleviate the challenges of connecting low memory, limited processing capability, and constrained power supply sensor nodes to the Internet. In 6LoWPAN networks, heavy network traffic causes congestion which significantly degrades network performance and impacts on quality of service (QoS) aspects such as throughput, latency, energy consumption, reliability, and packet delivery. In this paper, we overview the protocol stack of 6LoWPAN networks and summarize a set of its protocols and standards. Also, we review and compare a number of popular congestion control mechanisms in wireless sensor networks (WSNs) and classify them into traffic control, resource control, and hybrid algorithms based on the congestion control strategy used. We present a comparative review of all existing congestion control approaches in 6LoWPAN networks. This paper highlights and discusses the differences between congestion control mechanisms for WSNs and 6LoWPAN networks as well as explaining the suitability and validity of WSN congestion control schemes for 6LoWPAN networks. Finally, this paper gives some potential directions for designing a novel congestion control protocol, which supports the IoT application requirements, in future work.