I guess the next deciding factor would be if the Penguins can lure the Bears to battle in the water.
All bears can swim, but some better than others. Penguins still have the superiority of numbers, but they are shit on land, they can barely march on snow and ice, I don’t imagine penguins doing very well in the jungles of South America or the Andes…
After the war is over, there may need to be some small expeditionary conflicts.
For example IF the Bears win, we have Penguins in NZ (Some VERY close to where I live) BUT we don’t have any Bears ( with the exception of a few in a couple of Zoos )
Same goes for Australia…they have penguins, but no bears; well; except they have drop bears, but they are only bears by colloquial name, They are actually marsupials
Reading through this I think everyone skipped over birthing rates and how this would probably be a very long term war since there is no efficient transportation and weaponry involved.
Bears would probably not be able to recover from any losses (heck they can barely sustain their population without the war).
Despite what we think penguins would have a vastly better mobility by swimming away from danger and to new places. Bears can swim too but nowhere near the same range and agility, they have no chance of reaching islands and crossing seas.
It’s not all about the mele fighting. In a long term war bears would progressively die off chasing a phantom opponent who’s numbers never seen to go down.
Also my assumption is that both don’t become magically sapient and start using tools but they just have a instinctual hatered of each other for some reason and remaining wild with the same abilities as they do now.