The Barnes-Hut approximation for N-body simula tions reduces the time complexity of the naive all-pairs approach from O(N 2 ) to O(N log N) by hierarchically aggregating nearby particles into single entities using a tree data structure. This inherently irregular algorithm poses substantial challenges for performance portable implementations on multi-core CPUs and GPUs. We introduce two portable fully-parallel Barnes-Hut implementation strategies that trade-off different levels of GPU support for performance: an unbalanced concurrent octree, and a balanced bounding volume hierarchy sorted by a Hilbert space filling curve. We implemente these algorithms in portable ISO C++ using parallel algorithms and concurrency primitives like atomics. The results demonstrate competitive performance on a range of CPUs and GPUs. Additionally, they highlight the effectiveness of the par execution policy for highly concurrent irregular algorithms, outperforming par_unseq on CPUs and GPUs with Independent Forward Progress.