Hi,
A while ago Amir Ali Moinfar (and me) compared Harmony from R and the python implementation. We actually observed that the python implementation generally performed better, with higher biological preservation within cell types (fine-grained biological preservation) - this sometimes came at cost of somewhat lower batch integration, but often the batch correction was comparable while still having better fine-grained biological preservation.
The below plot is an updated version from the preprint https://doi.org/10.1101/2023.11.03.565463 (but the updated preprint is not yet available online).
