Can "worse" sound "better" ?

It looks like two of the cables are constructed of silver plated OFC copper, and I am not sure about the integrated -  it looks to be both silver and copper strands along with zinc and good shielding.   So, it is different than the other two and the hybrid strands and the shielding might make a difference.  How they are wound is obviously different between the three of them.  Best to go with your ears.  For what it is worth -  I found this comment online from the Lenco Heaven Forum by jloveys - 

"To sum it all up, preamp output impedance contributes to the ability to hear differences in cables between preamps and power amps. A preamp with a high output impedance will give the user the greatest possibility to hear differences in cables. A preamp with a very low output impedance will make all cables sound essentially the same. To put it differently, a very low output impedance preamp will be immune to cable effects and a very high output impedance preamp will enable the audiophile to spend countless months and dollars searching out that elusive ’magic’ cable."

The good news is you have lots of good options to explore.   The bad news is also that you have lots of options to explore so may take some time to settle on what’s best. 

Appreciate  your responses so far. 

@ghdprentice :  of course I did. A suggestion given by AI was to do with triple shielding of the Van den Hul the Integration Hybrid,and  its low capacitance, therefore suppressing noise. Would this be as simple? Maybe. But then many of us would use measurements as a starting point for a system configuration. And in my 50+ years I never did. I always listened. 

I trust my ears,  and am not influenced by market price, so the Integration is in use. The music just sounds great.  

Yes. The cheaper/low quality cables and component can sound better than more expensive/better parts component. To all them, the good sound is trial and error experience with some luck. 

All audio cable and audio component companies don’t know how to make a good sound cable and component. Some times, good cables and component (only marginally better) are made by accident, not knowing how that happens. I’m sure the better sound from the worse cable, OP hears, is small difference from other expensive cables. Alex/Wavetouch audio

First, trust your ears.  Sound quality is often not directly proportional to cost.  

Second, cable compatibility with a system as it relates to perceived sound quality is complex and I believe cannot be always predicted based on cable design, specifications, or cost.  However, there are some broad general rules of cable design that may explain what you are hearing.  
 

I have not auditioned any of the three cables listed, but I went on the website of each to look at their design. The Frey is a proprietary microfilament with minimal dielectric and should produce a fast, detailed and light, airy sound with stage presentation focusing on separation and air between images.  The Orchid is a low capacitance, low mass OHNO conductor.  This design should produce a fast, detailed, airy sound somewhat below the speed and detail of the Frey, but with more body and weight,  The Integration is a high mass silver over copper design.  The conductors are more of a traditional solid mass design than the other two.  This cable should, in comparison, produce more weight to the images, with slightly rounder edges and smoother transitions between images, focusing on venue depth and width rather than air in between images.  Instrument harmonics will be more evident, hall harmonics less evident.  

Which presentation is correct is personal preference.  What I describe as differences in SQ based on design is a generalization and many factors come into play.  Are my descriptions somewhat close to what you hear?
 

I recently had a similar experience where changing on cable at a key location had a profound impact on SQ.  I purchased an Audio Art Statement interconnect.   Previously I was using WyWires Platinum.  The Platinum is a Litz air core inductor design producing a clear, detailed, airy sound with excellent, but light imaging.  I replaced it at the streamer to DAC location with the solid core Statement.  Timbre, harmonics, image, stage depth, image density and macrodynamics all improved.  I list some, but not significant, transient leading edge, transient speed, air between instruments, hall decay, microdynamics.  The improvements outweigh the losses to my ears.   The Statement at this key location makes my system sound more like music at Carnegie Hall at half the cost.   
 

PS:  @ghdprentice I am now beginning to fully understand what I believe you have often stated, if I interpret your position and journey correctly.   Highly detailed systems that focus on extreme clarity and detail rather than musicality expressed as warmth and timbral accuracy initially impress but become fatiguing over time.  This one minor change in my system made the lightbulb go off and realize that is why you chose your components.