Make sure you get in a good test ride (or several!), and pick a bike you like from a shop you like.

CX bikes do tend to be a little heavier than road bikes. The wheels will usually be stronger, and have more spokes, and the tires/tubes being wider, will be heavier. I imagine even the frames may be made thicker/tougher (though I don't know for sure).

The Trek FX is a flat-bar hybrid bike, correct? There can be quite a few differences going from a flat-bar hybrid to a bike with drop bars, especially if it is set up more for racing. You may not be able to tell what needs changing and is comfortable until after quite a few miles on the drop bar bike. If you buy from a good LBS, they should be able to get you fit fairly accurately to begin with, and you'd only need saddle adjustments and a stem swap at worst.

For your height I would get something around a 56-58cm effective top tube, but that's a very rough guide. You can try an "at home" fit (have someone measure you) on sites like competitivecyclist.com.