I have CXN 2. I find the sound quality (especially dynamics and immediacy) of Spotify which plays natively (SpotifyConnect) on CXN better than that of Apple Music that plays through AirPlay. Expectedly so, as there are fewer stages when played native. I’d imagine the same deterioration through Chromecast. I don’t see lossless (resolution) a compensation for loss in sound quality. Also, please check if Chromecast plays Apple Music lossless… AirPlay doesn’t (unless played from MacBook with universal AirPlay setting).
By the way, no streamer has native Apple Music. Apple hasn’t opened up their service to streamer manufacturers for native integration unlike Tidal, Spotify or Qobuz.