Mostly SkisI feel somewhat qualified to answer this question. I've been skiing for 35 years and snowboarding for 18. My longest skis are 223cm and my longest snowboard is 210cm. I've never been clocked on skis, but my fastest measured speed on a snowboard is 69mph. In that speed run, my friend on skis did 74mph over the same track with the same starting spot (he's lighter than me).
I would say that in most conditions, a skier of comparable ability can outrun a snowboarder. The one exception from my perspective would be deep powder (assuming the boarder has a powder board on). The added float of the board, combined with the fact that you won't cross your tips, makes the board faster and more stable in powder.
Prazeres post on the first page of this thread covered most of the points. One thing of note is that speed is in large part governed by your brain. I'm faster than most of the people on the mountain, regardless of what I wear on my feet. Some people think I'm nuts, but its just a matter of comfort with speed. It is in part because of that comfort level that skis are faster. In an all-out tuck, you have a more stable, confidence-inspiring platform when you are on skis. The board at very high speeds (above 55mph) can start to get unstable and flop around. Eventually that will toss you on your rear.
Race course analogies are irrelevent IMHO. If a course is set up purely for boarders, then you will come much closer to parity. There is still probably a 5-10% advantage to the skier. However, the reference somebody made in another thread to a boarder entering a SG race in Oregon is irrelevant. First, I've hardly met any recreational racers from Oregon who are any good (Lynn Ott lives in Oregon, but she's a World Cupper, not a rec racer). I raced at Bachelor with Far West last year and crushed a bunch of their better skiers on a skier course with skier gates (painful and very slow on a board). When we set boarder gates and a boarder course in our local weekend warrior league, my times are pretty close to the skier times. Usually I come in near the 2nd tier of skiers. That said, I was never one of the fasted ski racers and I know that some of our ski racers in our league are very fast (faster than I would be on skis). We've talked around this subject at some length in our league in an effort to come up with the correct handicapping scheme. In the end, it is still going to be a random selection, but the NASTAR handicap of 10% for boarders is probably as good as any.
If anyone wants to challenge me to a race, come to Alpine Meadows and look for me. I'm one of the only people there on an Alpine Carving set up. In the morning, I'm usually riding a very long board and in the pm I switch to something that handles the crud a little better. Even in powder, you'll only find me in hard snowboard boots.