  We study the moduli space A_g of g-dimensional principally polarized abelian
varieties in positive characteristic, and its variant A_I with Iwahori level
structure. Both supersingular Ekedahl-Oort strata and supersingular
Kottwitz-Rapoport strata are isomorphic to disjoint unions of Deligne-Lusztig
varieties (see [Hoeve 2008] and [Goertz, Yu 2008], resp.). Here we compare
these isomorphisms. We also give an explicit description of Kottwitz-Rapoport
strata contained in the supersingular locus in the general parahoric case.
Finally, we show that every Ekedahl-Oort stratum is isomorphic to a parahoric
Kottwitz-Rapoport stratum.
