Apple's service has started in June 2015 and the gain is not bad for such a short time – although many predicted it would be much higher by now. Spotify has 75 million active users today but most of them are nonpaying. It has .had 20 million paying customers when Apple started and has more today.
Spotify annoys its nonpaying users with super noisy commercials, in the hope that you will pay for membership to make the annoying loud adverts go away.
Apple doesn’t offer the option to stream for free (no surprises there) but it has a better family plan. Spotify offers a 50 percent off on a second family member while the first member pays €9.99 / $9.99. Apple Music on the other hand lets up to six different family members, play the music at the same time, for €14.99 / $14.99. Apple offers its music service to Android users too. Most of this approach comes from Apple Music's recently acquired Beats audio company. Beats had a similar family plan and since iPhone is popular among Americans that can afford one, it might eventually gain on Spotify. Competition is a good thing, at least for end users.
Netflix wants your money, Spotify / Apple Music wants your money / Fitness tracking aps want to lock you in the subscription base. Modern smartphone and computer life is starting to feel like mobile phone carrier and Cable operator monopolists who suck money out of your pocket through their monthly subscriptions.