One thing I will say, what a player feels really depends on that player.
I admit that I am a weird character. I am a yoga teacher, I have been practicing and teaching for decades. From my perspective, a central part of that practice is FEELING what you are doing. Seeing how, putting yourself in semi-stressful positions and breathing as if you were relaxed feels: what different parts of your body feel, the emotions that come up as a result, feeling whether a particular position raises your energy level or causes you to feel more relaxed. And for sure, I can get myself (or someone else who I am working with) to be more relaxed or more hyped up depending on what the goals of the particular practice are. I can also help someone lower their blood pressure and slow their heart rate (temporarily) depending on how I have them practice.
So, for me, the feeling of the wood in the blade is not such a small thing. I have played with blades with harder and softer top plies. I have played with blades that are more and less flexible. If you put a blade that has a balsa core in my hand, and I can't see the wood but play with the blade to feel the blade, I can USUALLY tell you that the core feels like Balsa. Part of why I use an all wood blade is, I really like that all wood feeling and carbon blades I have used just have so much less of the wood resonance that I like to feel in my hand.
I love the way a blade that has a Limba top ply with a Spruce ply under it FEELS. But I don't like how fast the ball rebounds off the blade face when a Spruce ply is under a Limba ply.
I have used blades with harder top plies. I used a Timo Boll ZLF for a few years before 2015. Once I was used to it, it was quite a good blade. I never needed to change from using that blade. There are many really cool things about how the top ply being thin and hard (Koto) and the Zylon under it (with no carbon) being soft with a lot of rebound, causes the ball to really sink in and you can generate a TON of spin with that blade as a result and you also get this really cool, crisp snap on contact when you dig into the ball a little more.
Why did I change from that blade. One day I was hitting with a friend who had switched from a TB ALC to a DHS Hurricane King (Koto-Spruce-Ayous-Spruce-Koto I think that is the wood ply construction but I am not going to look and make sure my memory from 7 years ago is correct)

and when I hit with that blade it hit me how much I missed that extra feeling of wood resonance.
After playing with my OSP Virtuoso Plus (Limba-Limba-Ayous-Limba-Limba) for several years, Der_Echte gave me a Kim Jung Hoon (Nexy/Tibhar) blade. The top ply is White Ash. It is a 7 ply blade. I can't remember the rest of the plies. I set it up with every intention of using it as my main weapon even though I had no reason to change since my V+ works really well for me. I know, if I played with the KJH blade for long enough I would have gotten used to it and it would have been fine. But I just did not like the hard feeling of the top ply. I really didn't. I remember talking with NextLevel about it and he agreed that the KJH was much harder than the blades I had been using. At the time he was experimenting with the difference in impact depth for using harder top plies. NL is someone who also geeks out on subtle differences in playing characteristics of blades. He had a really good explanation for things softer blades and harder blades were useful for.
But I just knew, I had no real reason to change and really liked everything about the V+ so I went back to it after a few weeks.
Nate is a blade maker on this site. Maybe a year ago he sent me a PM and said he made a blade with me in mind and wanted me to take it, try it and see if I could tell him what I feel about the core (Red Cedar) he used for the blade and how it performed and how it was similar or different than the core I was used to (Ayous) and the rest of the ply construction was the same. V+ = Limba-Limba-Ayous-Limba-Limba. Nate's blade which I decided was "the Spin Machine" (I call the V+ "Holly & Phoenix Feather"), Nate's blade was: Limba-Limba-Red Cedar-Limba-Limba. The ply thicknesses and overall thickness are very close. There is a whole thread on the subtle distinctions between the two blades. But, one thing I can say, the Red Cedar (Spin Machine) was softer but I can go from one to the other without really caring because the important things about the two blades are so similar.
The Thread Where I Compare My Virtuoso + with the Nate Vortex Spin Machine
So, for sure, not everyone will care or notice the difference between blade constructions. A lot of Butterfly blades have almost the same blade construction with very small differences. But it really depends on the person whether they can tell the difference, care about the difference or not. In all honesty I can spin just as well with the KJH, the TB ZLF, a Viscaria, or my V+ or Spin Machine. It does take slightly different technique with the blades that have a harder top ply. And for me, I just like the big ball feel of the softer blades. But....I am confident I can feel the differences.
