Spotify has 75 million active users, 20 million of which are paying subscribers. Deezer has 16 million monthly active users and 6 million paid subscribers worldwide. Napster and Rhapsody have 3 million users, while Jay Z's Tidal service has 770,000.
Google Play and Rdio have not released official figures.
While Apple Music appears to have flown out the gates since its launch, the real test will be how it manages to convert these trial members into paying subscribers.
Subscription services make up 23 per cent of the digital music market and generated $1.6 billion in trade revenues globally in 2014, according to trade body IFPI. There is likely to be "substantial further growth potential", IFPI noted, driven by the increasing number of players in the market.
Apple Music's launch hasn't been plain sailing. Pop mega star Taylor Swift threatened to withhold her "1989" album from the streaming service after the technology giant said it would not be paying writers, producers, or artists during the free three-month trial. Apple quickly made a U-turn on the policy.
Users have also reported some bugs with Apple Music, a fact that Cue has recognized.
"We're aware that some users have experienced some issues, and we hate letting them down, but we're releasing updates as fast as we can to address those issues," he said.
But Apple has been on an extensive marketing drive with billboards and TV adverts. It has signed up major artists to DJ on its live radio station, Beats 1. And it is attempting to differentiate itself from the crowd through exclusive content. Rap mogul Dr Dre said he would release his new album exclusively on Apple Music and iTunes.