They have pretty much the same catalogue, 25 million plus in Tidal's case.
Pretty much, but not as extensive. Tidal does not have as large a catalog as Spotify.
But even Spotify has holes in its catalog. Songs by artist (some long dead) that are just not available. Fortunately, Spotify allows me to add my own tracks from my own collection and they integrate seamlessly into playlists.
That's one of the things Apple Music is probably going to be good at. It already has Apple Match, so not integrating with your own library would be stupid. That would fill out the holes, and hopefully it also allows Apple not to pay artists whose music you already own - thus leaving more for the artists providing music you haven't already paid for. The shouldn't be a need to pay twice.