Differences between xESMF conservative regridding and cdo remapycon

[chiaral]

This is not so much an issue but an observation I came across. If you think it should be reported as an issue I am happy to copy it there.

I was comparing cdo to xesmf for conservative regridding.
In particular I am using remapycon from cdo.

the 'desired_grid.nc' netcdf was created with the desired output grid. None of the files have bounds as part of the coordinate system saved in the files. Both desired and original have a regular grid (differently from the case of a GCM where sometimes the pole latitude grid values are different).

import xarray as xr
dsnew = xr.open_dataset('desired_grid.nc')
orignal = xr.open_dataset('original.nc')
regridder = xe.Regridder(original, dsnew,  method='conservative', periodic=True)
regridder(original).to_netcdf('regridded_xesmf.nc')

cdo griddes desired_grid.nc > target_gridspec
cdo -remapycon,target_gridspec original.nc regridded_data.nc

cdo = xr.open_dataset('regridded_data.nc')
xesmfd = xr.open_dataset('regridded_xesmf.nc')
(cdo-xesmfd).sum('time').pr.plot()

The magnitude of the differences is non negligible, but the issue is that it appears where there is a strong gradient in the field (i.e. orography by the coast).
It almost looks like one remapping occurs left to right, and the other right to left (does it make sense?)

cdo uses the YAC algorithm.

I didn't expect them to be identical, but I just wanted to hear your point of view on these differences.