AirPlay has the advantage of sending anything playing on your iDevice to the APE wirelessly, where CCA requires the app to have casting built in; most do these days, but Apple Music and a few others don't / won't. If you have a solid, interference-free wifi signal (unlikely in crowded apartment/condo complexes), it's a good choice, and very easy to use. However, it takes two or three times the bandwidth of Chromecast, which pulls the stream directly from the source.
I've found Chromecast can be difficult to get the stream started, though, and the app sometimes gets out of sync with what the CCA is playing, so you need to launch the Chromecast app to stop and restart the stream. When it cooperates, CCA has the advantage of not being dependent on your phone/tablet. AirPlay has the annoying habit of stopping the music any time you browse to a site with embedded music/video files, like allmusic.com, even if you don't start them playing, and muting the music for notifications of any kind. I believe this can be avoided by involving a NAS or PC in the mix, but I've moved beyond those years ago myself.
I use a different, all-inclusive system designed exclusively for streaming music, with a range of very high quality powered speakers as well, which has none of these issues, but many, many advantages, but is a bit more expensive. You gets what you pays for. I've tried 'em all, and will stick with the best.