I think Google has some kind of presence in Amsterdam (though not a big one), but they frequently have problems. I think there are two kinds of situation that Google Maps handles poorly:

* Bicycle route. They're just terrible at it. Better now than they were some years ago (when major bike routes were completely ignored), but still not great. They still prefer to send you along car routes instead of dedicated bike routes, even when those are shorter.

* Construction work (I don't think TomTom will be any better at this, though). Sometimes they do know construction work is ongoing; for example the Piet Hein tunnel near my house is closed for more than a year, and Google is aware of this. But they also don't show routes across the Amsterdamse Brug, which is still open, and the only real alternative. So instead they send you across crazy detours all over the city. But recently I was riding to Diemen along the Amsterdam-Rijnkanaal, and it turned out that dike was closed due to construction work. Big work with signs everywhere, but Google had no idea, and because there wasn't an easy way around, I had to take a big detour that would have been a lot smaller if Google had been aware of this.

There's no google office where I live, but google maps will show detailed transit information including exactly where on its route the bus you are waiting for is.

There's an attribution saying the data is coming from the local metro provider, who has their own interface for accessing the same data, but having it in google maps is nice as it integrates well with other navigation.

So I would say it comes down more to who has partnered with google to make the data more accessible.

Maybe more anecdotal, but I have had great mileage with google maps for navigation while driving too. The government department for land information does make almost all GIS data publicly available which probably helps too.