Pompei's will always present with cardiac problems and Cori's will not. For what it's worth, I have done a TON of practice qs so far and I haven't seen a single q about Cori's.
Pompei's: type II glycogenosis caused by alpha-glucosidase (acid maltase) deficiency, a lysosomal enzyme. Presents w/ severe failure to thrive, death by 2-4 yo.
Cori's: type III glycogenosis caused by debranching enzyme deficiency. Accumulation of glycogen w/ abnormal structure, moderate hepatomegaly. Compatible w/ near normal lifespan (contrast w/ Anderson's --> branching enzyme deficiency --> severe hepatomegaly, early death).
Also, first six glycogen storage diseases:
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V--Von Gierkes, P--Pompe's, C--Cori's, A--Andersons, M--McArdles, H--Hers