Avatar
1) When you say avatar you are assuming that creator of this Universe is separate from the creation and will take some Human form to put things which have gone out of order in his creation.
2) It is also assumed that as long as he is in Human form he will exhibit and confine himself with in the human limitations although there are some exceptions ( Krishna)
above points distinctly point to philosophy and tradition which believe in dualistic existence of atma and paramatma where in atma has a separate existence from paramatma.
swarga and naraka concept ( Garuda Purana) emerge from this line of thinking. these are distinctly vaishnavaite beliefs most of the vaishnava philosophies conform to this. although there are some followers of Vishnu in smartha( advaitha) they are very few.
Personification
1) Personification is nothing but giving shape to which is shapeless, Parvati is Shakti and shakti is sarva vyapi and is present all times and places.. For that shakti parvati is a personfication.
2) Parvati although human( debatable as Himalaya is a mountain) is not bound by human limitations. She still is Parvati and worshiped as such.
3) Sankhya and Advaita other saivaite philosophies don't believe in separate existence of atma and paramatma. According to most of them whole universe is the union of shiva and shakti so the question of avatar does not arise.
so the point is either you believe the first one or you believe the second one and when you compare both you cannot come to any conclusion. i personally believe in second one
PS: there may be some mistakes i would be glad if they are corrected and also i am open for debate on this issue.
Regards
Krishna