The frontal lobes are primarily involved in behavior, rather than
memory or traditional learning. In fact, patients with frontal lobe
damage often continue to test well in conventional IQ tests.
The parietal lobes, on the other hand, are involved in environmental
perception and visual-context behavior. Left parietal lobe injury can
result in a person having left/right confusion, problems with simple
mathematics, speech difficulties and problems writing. Right parietal
damage can cause someone to have difficulty doing simple drawings of
familiar objects or building simple structures.
Because of the complexity of the functions performed by both sets of
lobes, I'm not sure that any "one memory test" could distinguish
between the two types of injury or even determine definitively if
either were damaged. Also... keep in mind that there are actually 2
parietal and 2 frontal lobes, controlling four sets of capabilities
and behaviors, with some overlap from the perspective of an external