Scalable group key management (also known as group rekeying) schemes proposed in the literature can be classified into three categories: stateful schemes, stateless schemes and self-healing schemes. These schemes differ mainly on the interdependency of rekey messages and rekeying overhead. Logical key hierarchy (LKH) based approaches are stateful in that members should have received past rekeying messages to decrypt current rekeying messages. Stateless rekeying algorithms, such as subset difference based member revocation (SDR) mechanism, on the other hand, use keys sent during member registration/ initialization to encrypt the group key. In other words rekeying messages are independent of each other and consequently members going offline can decrypt the group key without having to consult the group manager.Furthermore, SDR rekeying cost is dependent on the membership during an entire session whereas LKH rekeying cost is dependent on membership of the group during a rekeying instance. In this paper, we study the advantages and applicability of stateful and stateless rekeying algorithms to different applications. We analytically compare the storage cost and the rekeying cost (number of unitsize encrypted messages) of LKH and SDR in immediate and batch rekeying scenarios. We implemented the two algorithms and simulated different membership scenarios to compare the rekeying cost. The simulation study shows that LKH performs better in immediate rekeying and small batch rekeying, whereas stateless rekeying performs better as we process membership changes in larger batches. In some cases, stateless rekeying was observed to be as inefficient as encrypting the group key separately for each member of the group. We also report on the effect of member adjacency on rekeying cost. Based on our analysis, we make recommendations in using group key management algorithms for various application sceranios.