You would not have the general gravel bike advantages of lower botton bracket for stability, more relaxed fork angle for better handling in loose gravel and more compliant frame for long distance comfort. Cross bikes are great for all out 40 minute sprints and weaving between slower riders. Gravel bikes are great for all day rides that do not require weaving in and out of tight packs of other riders. People do ride cross bikes for gravel, but generally most of the bikes are quite different.
The bike you mentioned seems to have more tire clearance than many older cross bikes, but generally cross bikes have less tire clearance than modern gravel bikes which is a big deal.
Those are good generalizations, but its hard to say they are "quite different," as there are racy gravel bikes (similar to cross bikes) and more endurance oriented bikes. I'd say there is a significant difference between an endurance gravel bike and a racy gravel bike, while not much difference between a cross bike and a racy gravel bike. For that matter, some gravel bikes are pretty similar to mountain bikes, while others are pretty similar to road race bikes (with fatter tires).
And, there are those of us who are dynamic riders and appreciate the agility of a bike with more aggressive geometry.