You might consider opting for neither and instead look for a so-called "gravel" or "adventure" bike. Both are relatively new categories, but either could be described as an "all-road" option. They're really road bikes that are meant for paved and unpaved roads.
Their advantages over contemporary road bikes include more clearance for larger tires and fenders, better accommodation for racks, and often, a more upright riding position. The advantage over contemporary cyclocross bikes would be a lower bottom bracket, more stable handling, and improved comfort.
Some examples include: the Surly Straggler, Raleigh Tamland, and All-City Space Horse.
My personal experience is with riding a Surly Cross Check (similar to the Straggler) with quality wheels and larger tires (700x40c Clement MSO, mostly) on thousands of miles of pavement and gravel roads. My experience has been that it's not appreciably slower than a road bike over long distances, and is far more versatile.
Good luck.