According to Reuters, Apple Music now has more paid subscribers in the US than Spotify.
A "person familiar with the matter" revealed that 28 million subscribers currently pay for Apple Music in the US, whereas Spotify has 26 million paid subscribers. However, Spotify still has more overall users in the US, thanks to the free tier, an option not offered by Apple.
That said, Apple isn't beating Spotify worldwide. A report from late last year showed Spotify had 207 million users worldwide, 96 million of which were paid subscribers (or in a trial for the paid subscription). Apple has about a quarter of that total number, or just over half the paid subscribers, at 56 million.
A big part in Apple Music's US dominance is the fact that there are over 101 active million iPhones in the US, and the app comes pre-loaded on the devices, as Complex points out.
Spotify and Apple have long been rivals, but recently things came to a head when Spotify filed an anti-trust complaint against the tech giant.