I don't have any experience using the old app, but I previously used Soundcloud's web product. The main purpose was to listen to music made by more esoteric artists. For more mainstream stuff, I turned to YouTube. Obviously this setup was suited poorly for mobile.

Now I use the Soundcloud and Spotify apps for roughly the same respective purposes (Spotify replacing YouTube). I prefer the simplicity of the Soundcloud app over the feature-rich but complex Spotify app. There's plenty of data not displayed in the Soundcloud app that might be shown in the Spotify app, but good luck becoming consistent at finding that data.

Overall I'm happy they cleaned up the app and dropped the old webapp features.