For starters, a cross bike usually has different brakes than a road bike, which allows it to accept much larger tires. A modern road bike is typically designed for short-reach dual-pivot caliper brakes that generally can't fit tires much larger than around 700x25 (or sometimes x28). Much larger than this and the tire will rub against the brake caliper arms. A cross bike using cantilever, linear pull, or disc brakes can usually go much larger. I'm not sure about that Felt, but some 'cross frames are designed for tires as large as 48mm.
Also, in the case of the cantilever and linear (aka V-brakes) rim brakes, they can be tuned to retract farther away from the rim when the brake lever is released. This gives more mud clearance than caliper brakes (not as much of an issue for discs), so the brakes won't clog up as easily.
Finally, 'cross bikes often have a different geometry than road bikes, including a higher bottom bracket for better ground clearance. A lot of people find that they need a frame one size smaller than their road bike to get a proper fit with a 'cross bike.