I like Spotify - but nobody with an iOS device will stick with them. Apple Music just offers better OS integration. And for Android, there's Google Play Music which is already pretty cool. Leaving the Windows Phone and Blackberry guys for Spotify: good luck :-/ What Spotify has going for them is the integration into services like WD Player, Sonos etc. - but Google also does Sonos, and it's a niche market. I'm sorry to see Spotify go down the drain - they were the pioneers and their service is really good.
On the contary, in the UK at least, Spotify has done a great job of being offered for free in various services. EG sign up to Vodafone 4G and you get the premium service, BT offered it at some point, plus others.
So they've a massive base of users who are getting the premium service for free.
That base, plus existing paying users, have been with Spotify for a few years now and have built up their playlists, their likes, their connections with friends on there etc....Apple Music simply doesn't offer enough incentive to move away from Spotify right now.
I am talking UK mainly here as I know Spotify only launched in the US last year, but have a look at the subscriber base for Europe and you'll see this is the equivalent of asking all the Man United fans in the world to jump ship and support LA Galaxy