How does wood hardness affect the sound of a TT on a wood TT platform?

I think the first thing you have to ask yourself is whether your tt is sensitive to what it sits on.  My Linn was extremely variable depending on shelf material, while my Basis is not.  I don't know what your table sits on now, but try a different shelf material like glass or corian or whatever you have and see if it makes a significant difference sonically.  That said, I truly do not believe one can predict whether they will prefer one shelf material over another without trying it.  There are just too many variables to make a blanket statement that harder wood does X and softer does Y.  
And even if you could predict, that doesn't mean you would prefer it.  

Hardness of wood is related to stiffness which is useful in resisting bending forces, I.e., isolating against rotational forces. Hardness is also an important characteristic of the cones the wood board should be resting on.

Elizabeth thanks for all that information on Butcher Block. My TT sits on a heavy 3 shelf MDF audio rack w/metal screw in poles. The feet are spiked . The floor is carpeting w/a cement base. My neighbor is the Apartment Laundry Room. There seems to be some inaudible vibration as some of my throw carpets over time move around. Both the TT and the Luxman 38 Tube preamp are a shade on the warm side. I think the Bryston 2.5 SST2 balances that out w/a neutral sound. Right now I'm looking at the Edge cut Maple and Walnut. The TT is fairly big so I will go for the 19"x16"x3" block. Just need to decide as to what feet to put on. 

@geoffkait OP might need springs with that vibration which changes everything!