A lot of it is a matter of fit. MTB racers run very aggressive fits, back angle about the same as a roadie. If you're sitting upright on your MTB it's either the LBS' fault for selling you the wrong size or model bike, or your fault for not insisting on an aggressive fit. You get an MTB with an aggressive fit, put narrow bars on it and 1" slick tires at 100 lbs and you're going up the road pretty good.
Back when I started doing long fast group rides, there was a guy used to come out with us on an old red steel rigid MTB with knobbies. He was over 6' and looked kind of funny over those little bitty wheels, but he had a flat back. He kept up just fine on 18 mph average centuries with 6000' climbing. Of course he would have been faster on a road bike or even the MTB with slicks, but he was dumbing the bike down to our level of riding. There's another local guy who competed on ultras who'd ride a full knobby rigid MTB on the one-day STP, just as fast as the roadies he'd paceline with. He wasn't particularly fast, never finished high up on the ultras, but he knew how to ride and how to fit his bike. He just thought a road bike was too easy. I could always tell he was around because of the sound.
Along that same line, there was a 2 who'd come out with us in winter on his fixie. He'd keep up fine on the hilly courses for a while, but eventually he'd have to break off after one too many 175 rpm descents. Something different for him to do in winter.
So there's more to it than just the type of bike. That said, of course most road bikes will be faster on pavement than most MTBs. But maybe not all. I've ridden some pretty sucky road bikes.
It's all about what you want to do, what your training goals are, what your expertise and talent is, and who you want to ride with. You want to go off the front of the Social ride on your new road bike? What's the deal with speed, unless you're riding with a group you can't keep up with? You're getting cups now but you want KOMs? Sometimes what you need is a slower group of friends.
You know what I finally did? I said screw it and started riding a tandem with my newbie wife. Took all the pressure off trying to be in the front group and I like it better that way. We have a lot of fun and still ride with the same group, just not at the front. Took about 3 mph off my average speed. So that's a good thing: the same ride lasts longer and thus is even better training. I think a lot of people on here could benefit by moving in that direction.