As far as i know Google beats Yandex in search (readed about this here http://habrahabr.ru/post/173351/). But Yandex got more detailed maps (google missed some objects / buildings). Yandex got Taxi app, public transport app, navigator, metrika (google analytics copy) and etc, etc, etc. For me as developer - yandex provides much better api documentation and examples.
But I can't understand - how can they force monopoly protest, being monopolists itself? Example - Only Yandex.Transport got API for public data (bus stops, Position Tracking) in Moscow. I am sure, that Google can protest them back. How Yandex had the nerve for this? Nothing personal, business only?
P.S. All above is about Russia context. In USA I don't know which maps are more detailed.