It depends on what you're using to search for the nearest Starbucks.
If you use the Apple Maps app to search for the nearest starbucks, it's gonna stay there and give you the directions you want from within that app.
If you use the Starbucks app, it will go to Apple Maps when seeking directions for the nearest store.
The Starbucks Mobile website (via Safari) will default to Google maps because that's what Starbucks has embedded on their site. You don't have a choice in the matter (except to use the Starbucks App, or search via Apple Maps app).
And if you have Google as your default search engine and search "starbucks locations" in Safari, well.. Google's gonna prefer Google Maps. That's just how it is. Google isn't about to promote a competitor.