We consider the problem of efficient particle advection in a distributed-memory parallel setting, focusing on four popular parallelization algorithms. The performance of each of these algorithms varies based on the desired workload. Our research focuses on two important questions: (1) which parallelization techniques perform best for a given workload?, and (2) what are the unsolved problems in parallel particle advection? To answer these questions, we ran a "bake off" study between the algorithms with 216 tests, going to a concurrency up to 8192 cores and considering data sets as large as 34 billion cells with 300 million particles. We also performed a variety of optimizations to the algorithms, including fundamental enhancements to the "work requesting algorithm" and we introduce a new hybrid algorithm that we call "HyLiPoD." Our findings inform tradeoffs between the algorithms and when domain scientists should switch between them to obtain better performance. Finally, we consider the future of parallel particle advection, i.e., how these algorithms will be run with in situ processing.