Joining streams is an essential and resource-demanding operation in stream processing engines. Recent works have shown significant performance benefits by offloading stream-join processing to hardware accelerators, including GPUs. As a result, a wide variety of GPU-accelerated stream join algorithms (SJAs) have emerged. However, existing works evaluate the proposed GPU-accelerated SJAs only in isolation, on different hardware, and not using a common workload. Consequently, it is difficult to compare different SJAs and select the best-suited SJA for a particular situation. In our paper, we shed light on the performance characterisJcs of GPU-accelerated SJAs. Our experiments show that each variant of SJA has its strengths and weaknesses and that ill-suited configurations of parameters lead to up to two orders of magnitude difference in throughput. Based on our results, we have developed a guideline for selecting SJA variants for different circumstances.