I have not been able to do a apples to apples comparison of the sound quality, since I use HQPlayer. With Deezer I have to use Chromecast SPDIF connected to SPDIF to USB converter to get the music to HQP, while for Qobuz I can use any of the UPnP clients like BubbleUPnP and/or mConnect.
Both have large selection of music that I like to listen to World, Jazz, 80's/90's music, Blues, Big band and some classical (just trying it out since Qobuz has such a vast collection). To my ears Qobuz sounds slightly better but I am not sure how much of the that is due to me using Chromecast for Deezer.
The one advantage that Deezer has over Qobuz is how it works with my listening pattern better. Deezer has what they call flow which is based around your favorites and you created playlist. They will play similar songs from their catalog. The downside for Deezer which is huge is that they make it very difficult to integrate with your two channel setup. All of the devices that support Hifi are more consumer based (Alexa, Google Home, Yamaha, Sony receivers, etc). I have been bugging them to make their API's for hifi available for folks to write additional software but so far no such luck. None of the mobile clients have hifi support so the only way to listen to hifi for Deezer is if you use their desktop application which is in beta state or you use one of the consumer product which do not integrate that well with my setup.
Qobuz is completely opposite to Deezer. All of their API's are published and anyone can write the front end to access their catalog, which helps with integration. You have just about any streamer out their that has built in client for Qobuz regardless of the cost associated with the streamer, from lowly Logitech Media Server with Touch or Rpi running LMS to Bluesound, Aurender, Lumin, Auralic, Devialet (sp?), etc. That options makes it very easy to integrate in your main rig setup. Since, I was already using BubbleUPnP and HQPlayer Embedded as UPnP renderer, it literally took me 15 seconds to get Qobuz up and running. All, I needed to do was enter my account information for Qobuz in BubbleUPnP and I was up and running. The other advantage that Qobuz has is if you like an album you can purchase it as flac file at discounted pricing depending on the subscription tier. For example, one of the album that Tom had posted in the what are you listening to thread was "Love Is Here to Stay by Tony Bennett and Diana Krall" you can purchase that album in 24bit 96kHz format for 10 Great Britian Pounds or Rimsky-Kosakov Scheherazade, Op. 35 for 10 GBP. The only reason for the GBP is due to my account being tied to UK based services. My assumption is that pricing will be similar in dollars once it is officially rolled out, since I have seen similar pricing for Euro.
I have been in communication with David Solomon who is one of the main guy trying to get Qobuz deployed in US (same guy who provided the license for the Oct. 27th event) and they plan to add the Deezer type of "flow" functionality in the future once they have US rollout completed.
So what I am doing is I listen to Deezer on the phone leveraging flow and add any song that I like to a playlist, convert that playlist to Qobuz using Soundiiz, which helps me around the flow issue and listen to the same music in the basement. If Deezer does not release the API or start integrating better with streamers I will most likely not renew my subscription once it is up for renewal. If they do I might keep both, since there are instances where one service has.
For folks who have Bluesound you guys might be in the best position to do a head to head sound comparision, since all three service is supported on the device. If Bluesound allowed me to send the stream to UPnP renderer I would purchase it in a heart beat, just so I can integrate with HQPe better for both Deezer and Qobuz.
Sorry, for the lengthy rambling post.