I find the original listing data functions (ListDatasets, ListFeatureClasses, ListFiles, etc...) rather clunky to work with compared to other options. The ArcPy Walk function is good for finding or enumerating data sets. In this case, though, since you are focused on specific geodatabases and want additional properties of data sets, like geometry storage type, I think the old Describe class is best.
The code below will go through a geodatabase and print out the data set names, types, and geometry storage if applicable.
import os
gdb =
full_path = False
desc = arcpy.Describe(gdb)
for child in desc.children:
datasets = [child] + child.children
for ds in datasets:
print "{},{},{}".format(
ds.catalogPath.replace("" if full_path else gdb + os.path.sep, ""),
ds.datatype,
ds.geometryStorage if hasattr(ds, "geometryStorage") else ""
)