I've been looking at canes on the Canemasters website and I've been wondering...

Are there inherent strength and durability differences between hickory, hickory with heart wood and pure hickory heart wood? Or is it a matter of aesthetics?

I'm not a wood worker or anything, but my understanding is that pure heart wood would be the strongest of the three. It is the densest kind of wood inside the tree. Dowels are typically made from heart wood, IIRC. I suppose it depends on species, but heart wood dosen't develop until a tree is rather old, so it's not a particularly renewable commodity, like getting it from younger trees that have recently been replanted.

If you want strength and are concerned about "renewability" go with the Asian staple; bamboo. Incredible stuff.

Follow-up.....Look on Ranger Rick site http://www.therangerdigest.com/Tips___Tricks/Bamboo_Walkin_Stick/body_bamboo_walkin_stick.htm. He has a brief article on bamboo walking sticks. It was rather interesting.

White Oak is always a good choice.

This could be totally false, although I have this idea in my brain that it takes something like 15-20 years for oak heart wood to develop in the tree.

White oak is an excellent choice, as LED said, but the OP asked about hickory.

As someone else said, the heartwood of hickory is (with all other things being equal) probably going to be stronger, but you're not going to have a weak cane with any of those choices. I think it's going to be more aesthetics than anything else.