I doubt there is much of a difference in quality. I think the biggest difference is stability. From my experience, streaming directly from the Sonos app is much more stable than using AirPlay.

It is two different methods of streaming. When using AirPlay2, your phone is contacting Apple’s servers to get the stream, and then sending that stream to the speakers. When you’re using the Sonos software, the speaker is reaching out to Apple’s server directly, and playing the stream, so effectively half the bandwidth in use on your local LAN. 
 

But the content being played should be the same. 

I agree with the other posters. Airplay 2 is not nearly as stable as using Sonos net to stream to your speakers. The difference is so stark in fact that I purposefully sold the two HomePods I had to go completely Sonos. 

As far as sound quality you are getting 256 AAC from Apple through Sonos net.  Im not sure about the Airplay stream quality but I did side by side test on my Sonos system between AACs and “Ultra HD” tracks on Amazon and heard zero difference.  This was on a Sonos Port playing through a very nice Aperion Audio/Denon speaker/receiver setup.  Frankly it all sounds phenomenal. If Sonos flipped the switch on Apple lossless or hi res lossless tomorrow, I’m not sure id even notice the difference.

Just my two cents. I’m a firm believer that the preferred sound quality aspect of a recording depends upon the listener when all is said and done.

To my ears streaming through the Sonos app to Apple Music everything is brighter with a push toward the mid-range on vocals. When playing the same recording via Apple Music over AirPlay2 the sound is not as bright with less push in the mid-range toward vocals. I personally prefer the latter which to my ears is more balanced. Granted on average the difference is negligible unless one is performing a critical listening test. 

I might add that the recording I played was R&B by a male trio. The vocals were harmonized with lead switching between tenor and falsetto. The vocal aspect mentioned may be less noticeable with rock and extreme genres.

I’d pick the one that was more stable and use that - everything other than unstable play, the brain can compensate for in the making of an enjoyable listening experience. 

Airplay also has the disadvantage of the handheld device having to be in the music play loop all the time.

Thanks for all the insight. Most times I play directly from the Sonos app but was Just wondering if you had an upgrade effect similar to using Apple TV music app through Arc. Sounds like it’s the opposite or just personal preference for a variety of reasons. Too bad Sonos couldn’t measure that in some way, it would be an interesting sales point. 

I’m as big an AirPlay fan as you can find but I find Apple Music through the Sonos app is noticeably better in every way playing to my stereo fives. I don’t notice the difference as much to my Ones which makes sense. I have zero issues with AirPlay stability and never have. If you do voice control to a homepod that does pull directly from apples servers by the way. 

I do not want to start another big lossless discussion.

But I have have an ATV4 and when I start Appel Music from the ATV4 and via AirPlay2 sends the music to my Sonos Port, then I am very satisfied with the sound quality ;-)

When you starts Appel Music via the ATV box, the music seems to be sent - and recieved as lossless via airplay2.

I do not think that lossless is played, when playing directly, from the Apple Music app to Sonos.

If you have an ATV and want to test this, then it is important, that you controll that the music really is started from the ATV and not playing via the iPad/phone.

But this sound change could certainly not be heard on smaller Sonos speakers.

I have Apple TV connected to Sonos Beam. In my experience playing lossless directly from Sonos app, I can hear all the speakers including rear speakers. But on Apple TV only on the  Beam.