Granite is about the hardest common stone you'll get, while marble is very soft by comparison. Marble is a metamorphed limestone, I believe, and highly porous. Stone makes a poor countertop, from a hygenic point-of-view, but is still popular as a prep surface for all it's other good properties.
Personally, I think granite is the best available choice in natural materials. Clean it as frequently and vigorously as you do a wooden cutting board, and keep meat prep to a single, specific location (for extra cleaning attention), and you'll love it for a lifetime.
Either one must be sealed, as Skuzzy pointed out, to prevent staining. And resealed regularly. Spend the money on the stuff with the longest durability, and reapply at twice the recommended frequency. Once stained, I don't know that there are a lot of options except stone bleaching agents...not a terrific result in all cases.
Didn't realize how thin the material was from the original post. If it's under 1" thick, definitely use an underlayment.
Hope it comes out nice!