Gravel bikes are going to be more endurance focused, CX more like a road bike or a crit bike.
I wrote more in a thread
: https://www.bikeforums.net/cyclocros...vel-bikes.html
but basically
Cross bikes: Quicker handling at the cost of stability.
Dynamically, a cross bike would be more agile, designed to be ridden more aggressively, accelerates and climbs a little faster, could corner harder/sharper (requiring more care on sweeping loose turns), less worry about pedal strike.
Gravel bikes tend to be more stable in loose terrain, and fast descents, a bit easier and more comfortable to ride, require a little more intention on turn-in (swinging wide too wide on very tight turns) and a generally more relaxed demeanor.
Cross can pull some high G-s in corners, where a gravel bike can to a loose sweeping turn without washing out.
Some older cross bikes are stiff and possibly twitchy and have limited tire clearance.
These days a good cross bike will be compliant, stable at speed, and take 40mm tires. The gravel trend has had its influence.
I love the Specialiized Crux, and Canyon Inflite. (both are available in Carbon or Aluminum).