I have heard ~ both types of platters, with the same cart though not on an oracle, but some generalizations may apply.
It is pretty uncanny how at least in some set-ups a different 'sound picture' is painted, we are talking 'shades' or nuances.
It MUST have to do with the material's resonance behaviour, because an especially well damped alu-platter (constrained layer) example TransRotor's alu-platter, does yet 'sound' different (if actually at all) to a not so well damped one, example Thorens's 2010 alu-platter, and these vs. some 2" acrylic platter, all on mass, un-sprung tt's.
I had some more confirmation talking just a few days ago to a very experienced acoustics designer/engineer.
In fact he uses a simple test, by taking a music-box (German: "Spieluhr') and places it on the different materials he evaluates, and due to the little wind-up music-boxe's frequency range (the melody it plays), he can tell the colouration the material it is placed on imparts on the music signal. I thought that was rather interesting.
Back to platters. Acrylic = damped behaviour and imparting a minute plasticy signature (you need bat-ears to confirm it I guess). Alu-platter not using constrained layer damping of any kind = more brilliance, openness, but a minute metallic signature, some would call it 'faster' sounding.
Alu-platter constrained by vinyl as in Transrotor Z3 = close to Acrylic but slightly more 'open' and no easily perceivable signature to my ears at all.
TW Dacron TM with copper constrained layer = ???
I can only guess that it will sound just that bit less closed-in (nice word for dead plastic) then plain Dacron unconstrained.
If in doubt, get a music-box, listen and see what you shall find ---- and it might be 'zilch' to your ears after all.