Your best option is to listen to both, preferably through your DAC and amp of choice (and speakers if that is possible).
I listened to the CXC vs CDt (not the CDi-XR) and I could hear more detail from the Cyrus. I ran both through the Dacmagic 200 , Vincent SV200 and B&W 706 S2 and sub. In the end I went with the CDt and an 82 DAC QXR. I already have an upgraded Arcam rBlink so didn't need the Bluetooth.
I've read a lot about the reliability etc. of the Cyrus mine have been fine. The CDt is noisy loading but quiet as when playing. I have a lot of the old three-inch/mini-CDs still, hang over from the eighties/nineties, and they load fine too. I've had two CDs that got rejected but a warm breath and a 'polish' shorted that out.
Having recently upgraded one of my two systems, and spent (for me) serious cash, the absolute key was/is to listen to the combinations and if you can in your home and not the acoustically perfect listening room where everything sounds fantastic!