Apple doesn't have to "win". Apple just needs to have something good enough for them to tightly integrate into their other services. Bing's purpose for Microsoft is both to be a revenue generator and to not be dependent on Google for search. Apple's only motivation for Maps is not to be dependent on Google for Maps and for integration into iOS.
Every time someone doesn't use Google Maps, Google loses ad revenue. If people don't use Apple's maps, Apple has lost nothing but a few bragging rights.
If people don't use the app, it gets worse for other users of the app (network effects for traffic, corrections, etc.), which means fewer people use the app, and so on. Ultimately, if the quality of the app is bad, Apple remains dependant on others for mapping services.
Every time someone doesn't use Google Maps, Google loses ad revenue. If people don't use Apple's maps, Apple has lost nothing but a few bragging rights.