We just completed a marble floor restoration in a private residence in Toronto where the finish to the floor was honed. Honed finishes tend not to show the wear as quickly as polished ones do, however all finishes still need to be properly cared for.
The honed surface finish is more open (the pores on the surface) than that of a polished finish, and thus dirt collects easier in the pores resulting in increased moisture absorption over a shorter period of time. The honed finish still requires routine and regular cleaning and sealing.
Marble is prone to etching (dull marks on the surface), wear (scratches on the surface from foot traffic and objects dragged across the floor), and general wear and tear over time. To restore the finish requires sanding and re-honing (or polishing) to remove etch marks and wear and sealing to provide protection against staining.
For more information on most common surface problems, please follow the link: http://marblerenewal.ca/most-common-surface-problems/