I've measured the properties of a lot of different pieces (and species) of wood. On average EIR has similar stiffness along the grain, but is less dense than BRW. IRW also normally has much higher damping than BRW or Padauk, although it's usually lower in damping than walnut or mahogany. These are natural materials, of course, and there's a lot of variation and overlap in properties.

Damping is the rate at which the material dissipates vibration energy. It often seems to me that the damping of the wood sets a sort of limit on how low the damping of the structure that's made from it can be. It's very easy to make a guitar back that has high damping out of a good piece of BRW: factories do it all the time. A good maker can usually figure out how to get the best out of a piece of wood, and can produce a better instrument from (high damping) maple than some made out of (low damping) BRW or Pernambuco.

It also seems to me that the mass of the back can be more important than the damping. After all, it's only 'losing' energy when it's vibrating; if it's too heavy to move much it's not losing. I've heard some very good things about African Blackwood, but the stuff I've measured has high damping. The same is true of Morado/Pau Ferro, which is as dense as the ABW, and I've made some nice guitars from Morado.

If you're looking for a wood that's like IRW in terms of density and stiffness, but has the damping of BRW, go for Black Locust.