Geometry and fork travel, and quality of the fork are some differences. The 2016 Crosstrail Pro Disc has a Suntour coil-spring for with only 50mm travel, whereas the 2016 Crave Expert at the same price has a Reba SL air fork with 100mm travel. The longer travel is more suited to offroad riding, plus the 100mm is a much more common fork travel distance making it easier to find replacements and upgrades.

ETT is shorter on the Crosstrail at 585mm versus 604mm on the Crave, for the two medium frames. That's enough of a difference to matter. I once owned a first-year Crosstrail. The shorter top tube in comparison to my mountain frames was mildly annoying and forced me to run a somewhat longer stem than I would have preferred to run at the time.

Tire width. I haven't examined a Crosstrail closely in a while, but I'm pretty sure the rear triangle of the frame constrains tire width. That appears to be the case from looking at the photos, and my guess is that you can fit wider tires to the Crave.

But I'll agree w/the OP that a bike like the Crosstrail can go pretty much anywhere that a similarly-designed mountain-bike can go. Sure there are differences, but a halfway decent rider would compensate for them and keep on going.