Try doing a CX race (I mean a proper one, not the Three Peaks) on an XC HT. You’ll be back of the pack unless you’re VERY good (Pro-Elite standard). A proper CX race bike is set up to be as fast as possible over a 1hr circuit of the type seen in Belgium, Holland, etc, mostly fast, undulating, not-too-technical terrain. For the same reason CX bikes are banned at events like Mountain Mayhem where the terrain is very similar. A CX bike would be far faster. Proper CX racing is a niche within a niche, it’s VERY specialist and to do well you need the full set-up (2 bikes, several sets of wheels, a pit crew)
The type of CX bikes commonly sold to the general public now are much more all-round and versatile bikes, good for light touring, commuting, most off-road etc. On a proper off-road trail ride (pick any trail centre as a rough guide), they’d probably be slightly slower overall than an XC HT and not as much fun over the descents and jumps.