Spatial Join order of layers is not symmetric?

Question

I am doing a spatial join between two datasets ("LUI" and "Parcels") with the Are identical to match option. Since I'm looking for exact matches, I would think that the order of datasets does not matter -- that is, I could put LUI as Target Features and Parcels as Join Features, or I could put Parcels as Target and LUI as Join, and get the same result. Strangely, there is a single polygon which only shows up in one of the joins.

Here is how most of it looks. The crosshatching in both directions shows both versions of the spatial join, and Identify shows 4 entries.

Here is the outlier:

If I select the underlying two polygons and double check the geometries by direct comparison, it says they are equal as well:

with arcpy.da.SearchCursor('LUI2020_Kendall', 'SHAPE@') as c1:
    for r in c1:
        with arcpy.da.SearchCursor('stacked_parcels', 'SHAPE@') as c2:
            for q in c2:
                print(r[0].equals(q[0]))
>> True

The other things I checked are that it doesn't make a difference whether the two source layers are in the same GDB or not, and that the source layers have the same CRS except for the Z precision (and there is no Z element in these shapes). I am using ArcGIS Pro 3.5.2.

Any explanation of why this behavior is different would be greatly appreciated!

samuel_e · Answer

Thanks for the response. In this case, we do want exact clones (comparing parcel years where PIN might have changed but geometry did not).

I understand there are ways to get around this, for example perform both spatial joins and merge the two layers. I'm more curious right now about why the spatial join would have different behavior in the first place.

DanPatterson · Answer

Spatial Join (Analysis)—ArcGIS Pro | Documentation

have there centers in, or largest overlap might be a better option since matching "exactly" could be a hard case to handle unless both are true clones in all respects