What is the difference between cyclocross-bikes and road-bikes?

I concur with many of the answers in mine research .Just a couple of things I'd add to the conversation.

Disadvantages

Cross vs road geometry: In general cyclocross bikes have a shorter top tube, taller bottom bracket, taller bar position, and a more relaxed front end. On the road this means the bike won't handle quite as crisply as a pure road machine. There can also be challenges with road-related fit if you're using the bike only for the road after riding a road frame for a long period. Additionally, cyclocross bikes frequently are designed for 1 hour efforts meaning they can lack bottle mounts vs. road bikes.
Gearing: Mostly covered above. If you're a strong rider, you may find you're undergeared in fast group rides.
Other component-based implications: You won't get a decent race tyre, the brakes (if pure canti and not long arm canti or disc) are not as strong. Canti brakes are also harder to adjust and maintain over time. Bars are also usually wider on 'cross bikes.

Advantages

Cross bikes are built for the worst. This means overbuilt for road use. Better seals, more durable components (at the price of some weight), and external cable routing (which is easier to maintain) dominate the 'cross scene.
Flexibility. If you do have limited space, you can change the behavior of a cross bike dramatically with just a change of wheels or even a change of tires. I do know a few people who race 'cross bikes all year round on the road and in 'cross.
Gearing: If you aren't fit, 'cross bikes can offer a bailout gear you won't necessarily find on a race bike.

During winter 'cross season I ride my 'cross bike in group rides, race it on the weekends, and do the occasional early season crit on it as well. If you can only buy one bike and you aren't riding impossible singletrack every weekend, it's hard not to recommend a cyclocross setup.