MQA was supposed to give a high res solution at a lossy file size. But it does not sound as good as a real high res file. Qobuz high res sounds better. A high resolution file downloaded from hd tracks played from a local network storage also sounds better. Apple to apples comparison.
End of the day, it all depends on the quality of the original mastering. CD quality if mastered well sounds really good. Badly mastered music irrespective of file resolution sounds equally bad.
Overall, this high resolution digital is a mixed bag. Some albums sounds way better than 16/44 and some not so much. The ones that sounds way better is surely not because of the higher bits only. The big factors that contribute to the quality could even be a different master, different process used when they made the new file etc.
One thing to keep in mind is the normalising of album quality that happened when high res digital and streaming came into the picture. In past, while buying cds, they quality used to wildly differ based on which region you were buying the cds from. I have many duplicate cds from various regions - Europe, Uk, India, Japan etc. They all used to sound quite different. Some were really bad. Most of the horrible ones were printed in India. But if you listen to same album on Qobuz, it sounds more or less as good as the best version of the cd out there. That is a blessing. In some cases the best cd version will sound better. I have some Japanese cds of dire straits. They sound better than Qobuz.
If a good version of the cd is played from a very high end transport, they will trounce the streaming thingy. So, people who own a large collection of the best versions of cds of all their favourite albums and they play using a dedicate transport into a dac, will always say that the cds sound better than streaming. It gets weird as you go deeper and deeper.
MQA should be the least of our worries!