Whitch is right :spherical area or cartesian area

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I am asking a theoretical question here. I was comparing the areas calculated by MapInfo with the ones calculated by ArcGIS and I always add differences. When Googling that, I ended-up to that link explaining the differences : Area calculation MapInfo/FME. Basically, the default method for MapInfo uses spherical while the defaut method for ArcGIS is cartesian. When I changed the default parameter of both GIS, I ended-up having the results of the other GIS, so both are correct.

But now, whitch result is better or I'd rather say « righter », spherical or cartesian?

Thanks

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T_Bacon On BEST ANSWER

In simple terms, spherical area takes account of the curvature of the surface of the earth whereas cartesian measurements are calculated as if the objects were on a flat plane. Generally speaking this means that spherical measurements should be more accurate.