It is not a race to become the universal map. When Steve Jobs was breathing, there were a few fierce words about 'Android'. Having Google Maps or a Google browser on the phone was to be avoided at all costs so Apple shopped for maps and put something together so they would not be at the mercy of Google deciding to discontinue their maps app on iOS/Safari. So the Apple maps were never born out of vision, just spiteful thinking and a perceived need to have indigenous maps that were not supplied by the old sparring partner (Microsoft) or the evil Google.
I think that the Apple map product was designed in that era of skuomorphic thinking that went on until recently in iOS. So the maps are designed to be a familiar map, much like the atlas you had as a kid when it comes to typography.
The Google Maps evolved from looking like paper maps a long time ago and are about showing you the information you want, not everything that can be crammed on screen. This challenges us to think about how we see the world, for a long time 'A-Z' maps were the thing and you had page numbers and 'square' numbers, e.g. B7, page 126 instead of 'hyperlinks'. Apple maps are more in line with that 'old persons' way of dealing with cartography issues, the Google maps are pioneering a better UX for visualising the world.