Tasking promises a model to program parallel applications that provides intuitive semantics. In the case of tasks with dependences, it also promises better load balancing by removing global synchronizations (barriers), and potential for improved locality. Still, the adoption of tasking in production HPC codes has been slow. Despite OpenMP supporting tasks, most codes rely on worksharing-loop constructs alongside MPI primitives. This paper provides insights on the benefits of tasking over the worksharing-loop model by reporting on the experience of taskifying an adaptive mesh refinement proxy application: miniAMR. The performance evaluation shows the taskified implementation being 15–30% faster than the loop-parallel one for certain thread counts across four systems, three architectures and four compilers thanks to better load balancing and system utilization. Dynamic scheduling of loops narrows the gap but still falls short of tasking due to serial sections between loops. Locality improvements are incidental due to the lack of locality-aware scheduling. Overall, the introduction of asynchrony with tasking lives up to its promises, provided that programmers parallelize beyond individual loops and across application phases.