I have a TEAC 701T and a Berkeley Reference MK II MQA DAC and I have bought 18 MQA CDs (I just counted them) to test the format. Most of them sound pretty much identical to the regular CD. An example is Rapture by Anita Baker. This is a great sounding CD and the MQA version sounds very close if not identical. On the other hand I tried a couple of Doobie Brothers titles and OMG, what a difference. The MQA versions sound clearer, more detailed, and overall much better than the CDs. I went back and bought all of the Doobie MQAs I could find.
I'm sure that the sound of the Doobie MQAs was due to remastering but they are the best sounding versions I have. I also have most of these tities on CD, SACD, and vinyl and the MQAs are absolutely superior.
My take is that the MQA format itself is very close to the original CD in SQ but sometimes you can get a remaster than sounds clearly better.