Cyclocross bike as fast as a roadbike?
TL:DR Get the CX Bike, you'll love it! You get three bikes in one, without trading in any noticeable performance on the road. This answer is subjective and based on personal experience, you have been warned:

I have a CX bike that is used as a do-it-all bike, and I love it.  For almost all aspects that concern any non-professional cyclist a CX is as good, or even better when compared to a "true" road bike, with some nice added benefits. Here's why:

I use it to commute because:


It is fast. It is light. And robust. You can get a second hand one (or similar) for 400$. 
It has enough space for comfortable road tires (28 wide fits with ease)
Offroad performance is still great without the use of noisy/bouncy knobby cross tires (I use 700c x 28 Schwalbe Delta Cruisers, a perfect allround tire with enough grip on gravel while still fast and comfortable on the road. 25% of commuting is on gravel/ hardpack sand. In 3000km on these tires not a single flat, plus they are quite affordable!)
Enough room for mudguards in rainy weather, due to the frame spacing and the cantilever brakes.
In rainy weather, the brakes are designed to keep functioning and not clog up with mud, leaves etc. It is true that canti's are slightly less powerful in dry conditions compared to modern road brakes. But they have proven very reliable under all conditions.  Discs would be even nicer.


I use it for long vacation trips


again because of the comfortable tires
The possiblity to carry quite some stuff on a seat post mounted rack, without worrying about damaging the bike or cracking the frame, since CX bikes are built for strength and durability.


I use it for riding with my friends (who all ride very expensive shiny carbon bikes) because:


We are not pro's, we ride fast, but always for fun. The 700g weight difference (if that) between my bike and theirs does not matter to me. How much beer we had last night has a much bigger impact on how fast I am. 


I even use it for light MTB duty because:


I have a set of old pretty beat up off-road only wheels for the bike with CX tires, swapping wheels takes only 1 min. thanks to the canti brakes.
The bike is very fast on grassy/forest singletracks, as long as there are not too many braches, steep climbs or large drops you can easily keep ahead of most "real" MTB's. Of course this is only within reasonable limits, I am not saying a CX bike can do any seriously challenging terrain.
In deep mud, the thinner CX tires cut through the mud and ride on the solid surface beneath the mud, where the MTB's float and lose traction. Up to about 3 inches of watery mud on top of a more solid surface a CX bike will be faster than wide MTB tires. 


On top of all this, here in Europe CX is pretty much a niche market. Most road bikers won't touch a CX bike, because they think they are slow (not true, as long as you don't race for a living). High end new CX bikes are all that leave the shops, those bikes then end up on the second hand market after a few years, where nobody seems to want them, thus you can get a much nicer bike for your $.
All parts are interchangeable with road bikes too, apart from the brakes, so upgrading is always an option.

All in all, CX bikes are just more rugged road bikes that seem to get very little attention by the mainstream road crowd. Too bad for CX manufacturers, but good for us no-nonsense bikers who are looking for a 3-in-1 bike solution.