Are granite/marble floors safer than hardwood or bamboo floors that contain aluminum oxides?
Granite can emit radon, which has been known to cause lung cancer. Also, granite and marble are not renewable, so they are not very green as far as products go.
Hardwood or bamboo are much more renewable, but can contain aluminum oxides. Aluminum is believed to be linked to Alzheimer's disease. However, aluminum oxide does not become airborne and is only dangerous when you eat it or if it is absorbed through the skin. Radon, on the other hand, is dangerous when you breathe it.
Not knowing about the location of the floor, I believe hardwood might be better.
There are floor coatings out there that are based on ceramic and are low-VOC products. You would have to purchase the wood unfinished and finish on site.
For more information:
Read Mary Cordaro's Q&A "Is bamboo flooring with aluminum oxide finish considered a green choice?"
Also, read Randy Potter's Q&A "What is a reasonably priced hard-surface flooring with low VOCs?"