I haven’t heard the X-Statics but the tweeter in the CST-1 is planar magnetic, so my guess is the CST-1 would be the over all better sounding speaker.
Whether it is better sounding or not is debatable. Different, yes. Better, not so sure about that. I built both the N1X, which uses the Neo3 PDR planner driver and the X-LS Encore, which uses the Peerless driver that's used in the X-Statik.
To keep the comparison as close as possible to apples to apples I built the X-LS Encores crossovers like the N1X (i.e. point to point wiring Sonicap capacitors, Erse XQ inductors, and Mills resistors), used tube connectors on both, used the same flared port in the Encores that the N1X uses, and put No-Rez and AcoustaStuff in both pairs. The only thing I couldn't keep the same was the woofers. The N1X uses the M130X woofer while the X-LS Encore uses the M165 woofer.
There were differences between them for sure. The N1X with the planner magnetic tweeter was more detailed while the X-LS Encore with the Peerless dome tweeter was a little smother.
There was no way I could pick a clear cut favorite. It depended on the type of music. For example, with detailed music like classical I preferred the planner tweeter while with jazz I preferred the dome tweeter. So which tweeter I liked best really boiled down to what mood I was in.
Don't take this to mean I'm saying the planner tweeter was not good with jazz or the Peerless not good with classical. Both are exceptional with any type of music I listened to.
Danny has a floor standing models for both of these tweeters, the N3s for the planner magnetic and the X-MTM Encore for the Peerless. These two models have more differences than just the drivers. The N3s are a smaller transmission line while the X-MTM Encores are larger ported cabinets.
I have built and listened to both of these floor standers side by side. The X-MTM Encores are very good sounding speakers. However, I would choose the N3s any day.
As for what others have said, if you like black cabinets but want the N3s you can get the CST-1s and replace all the components with the N3 kit for less than you can get cabinets built with this level of finish.