Mountain Biker wanting to change to cyclo or road? Which one? I ride an inexpensive Trek modified mountain bike and I spend some of my ride on the road and some on the canal, which of course is rather flat. Sometimes at the mid point of my ride I will decide to get off the canal and get onto road with lots of hills. Obviously the mountain bike is not made for this however I enjoy that challenge. Right now I am looking at the Crux Elite EVO. Would that be a good choice, is it worth the money and how much faster would I be on it? Or road bike???
I've had a hardtail mountain bike for a few years, and used it for all kinds of rides -- singletrack, rail trails, roads.  A few months ago I got a cyclocross bike (Norco Threshold) in addition to the mountain bike.  So I'm in pretty much exactly the situation you describe.  

I am enjoying the cyclocross bike and I feel like it's made me about 3-4mph faster.  I am surprised that I like the drop handlebars better (more comfortable) than the straight handlebars on the mountain bike.

I already had a set of slick tires for the mountain bike that I installed for road rides, and switched back to knobby tires for singletrack rides.  If I only had knobby tires, the speed difference would probably be even greater.

The Specialized Crux that you're considering seems like a pretty good choice.  It has 38mm tires out of the box, which is nice especially since you're used to mountain bike tires.  Tires of that size have a much less harsh ride than thinner tires (28mm), and don't slow you down (people used to think that, but research has shown that it's not the case).

Two things to consider about that bike: The brakes are cable/hydraulic hybrids; there is a brake cable that connects to a hydraulic piston.  I'm not sure if those are as good as regular hydraulic brakes; there is probably a bit of friction in the cable.  The other thing is the gearing: for hills you might want an 11-32T cassette instead of the 11-28T.  Depends on how strong you are and how steep the hills are. 

If you care about riding in the winter, go to a Specialized dealer and ask if you can install fenders on that bike, and what size tires will work with fenders.  To attach fenders, you generally need eyelets (threaded holes in the frame). If the frame doesn't have any of those, it makes it very difficult to mount fenders.