Which material sounds better for speakers construction? Wood, Ply or MDF?

Amongst hardcore DIY speaker builders, "Baltic Birch" is considered the best plywood. It is void-free, 13-layer 3/4", often in 5' x 5' sheets, though sometimes 4' x 8'. A great enclosure can be made of an inner box of Baltic Birch (with cross-braces also made of BB), surrounded by an outer layer of MDF, with a thin layer of constrained layer damping material (such as E-A-R Isodamp) between them.

MDF first then veneer, not plywood. Almost all plywood has core voids, even pricey Baltic Birch. Unless you specify all B grade veneer, but even those will have defects in the veneer faces.
B&W uses wood veneer sheets to build their enclosures, probably 1/10" or less, maybe even 1.5mm sheets, so yes using 12-13 sheets will get you 19mm or 3/4" close. Using veneer sheets allow them to bend the form to create their desired shape.

MDF is homogeneous, same density from face to back, all throughout, no core voids. Can be moulded and shaped easily, painted and or overlaid with wood veneer and stained for a super high end finish. The boxes using MDF are perfectly matched meaning both speakers will be identical to within set tolerances of probably +/- .03125".

I think it's close between ply and MDF. Construction matters however.
The best MDF I have seen use 1" thick layers to build up the case, with each layer using a different bracing topology. This yields an incredibly stiff and inert cabinet. but is very expensive and produces tons of dust.

Best left for those with access to CNC machines. Still, it's a lot cheaper than billet aluminum. :)

Best,
E

Try Magico they use aircraft grade aluminum as it sounds much better and is neutral.Mdf is history for state of the art speakers.

we made some speakers from   Bamboo 1 ply, 
the very solid material  ,and good acoustic performance