My CX and road bikes are similar in terms of the average speed over tarmac, but they do definitely feel different.
Oh, I should say that my roadie is a Secteur, which is probably not what you were meaning by a "full roadie" in the OP. I'm also comparing the Secteur with 25m tyres and the Tricross with 32s.
IMO, the roadie feels lighter, snappier, more responsive and it transfers much more of the road surface up through the saddle and bars. Whilst the saddle height is similar, I have the bars set a few cm lower and a few cm closer to the saddle. It certainly isn't uncomfortable, I've spent 5 hours in the saddle without a problem, but it isn't that relaxed either.
Conversely, the CX, on 32mm tyres, feels smoother, easier, less edgy, like it's had it's mug of Horlicks. The steering is still precise, it's just lost that twitch that you get from 100+psi. The drops are still low, but they are "I could ride here for hours" low rather than "Oooo, that twinged after 5 minutes" low.
Strangely, IMO, I've often ridden the two over the same course (commuting etc) and the times are within a gnat's whisker of each other. The larger tyres of the CX mean that I ride more consistently, I'm not watching out for dodgy surfaces, I'm not braking for speed humps, I just ride through the lot. That also means that the (minimal) extra weight of the CX isn't a factor over distances, as I'm not braking and pushing so often, I can maintain a cruising speed.
Other differences which may be more important than the BB height but which isn't strictly about the geometry, are that many CX bikes use a full or semi MTB gearing set up and the braking systems are likely to be different, with 32 teeth on the rear sprocket not unusual (rather than 25 on a road bike) and cantis or disks on the CX.