Pretty much every building material has some kind of health concern linked to it - for example, asbestos in insulation and lead in paint. Recently, granite and concrete have made the news; granite for emitting levels of radon that may be unhealthy and concrete for containing heavy metals [sources: CBS, Kolich]. Both materials may potentially emit pollutants into the air and water when they're being ground and sealed, and neither one is significantly healthier for the environment. If you want a truly green countertop material whose production doesn't produce a lot of greenhouse gases, you should look at materials like recycled aluminum or bamboo
Concrete and granite are both sturdy, high-quality options when you're choosing a countertop for your new kitchen. Each one has its own aesthetic draws. Concrete can be personalized to any taste by pouring it and molding it to your preference of shape, or by mixing different pigments and stones into it. You can also imbed anything you want into a concrete countertop: from drain boards and knife slots to your coin collection or anything else you want to display. Granite, on the other hand, is natural stone that varies in pattern and color based on what part of the world it's quarried from.
Neither option is cheap. Both concrete and granite run from $50 to $100 per square foot, and if you want custom concrete built-ins or higher-end granite made from a single slab, that price is going to go up. One clear drawback to concrete is that because it's a porous material, it's susceptible to staining and you'll need to get it resealed more often than you will a granite countertop.