MQA vs iTunes CD sounding quality is an interesting question as there are many music file formats that iTunes supports like MP3, AIFF, WAV, MPEG-4, AAC and Apple Lossless (.m4a). If you are comparing MQA with iTunes Apple Lossless that may be a close match with source material being the same... From what I understand MQA is remastered while Apple Lossless is basically a red book CD copy for the most part... The other issue is what the iTunes player and the hardware it is playing on doing to the signal (think AirPlay for instance)... iPhone or Mac internal DAC or an external DAC... There a lot of things to take into consideration from the source to the destination in the signal chain...
Perceived quality will be a mixed bag when comparing apples and bananas... ;^)
I run Audirvana Plus, Tidal HiFi MQA and DSD128 from a MacBook Pro over local wifi (DLNA/UPnP) to a BurrBrown based DAC into a Tube Pre, a McIntosh SS Amp and MartinLogan ESL speakers...