From everything I've read about the SpaceShipOne project, there's no way it'll break the Mach 6.7 speed of the X-15. It simply isn't designed to go that fast. If you recall, that particular X-15 suffered serious structural damage on the fastest flight. It never flew again because the X-15 program was canceled before it could be repaired. The X-15 was made of Inconel X, a type of stainless steel, and for the really high speed flights, they added an extra coating of an ablative material. SpaceShipOne is designed for much lower thermal loads.

Rutan did build the plane that set the distance record. I saw it again last week, along with one of the two surviving X-15s. As you posted recently, he's working on another round-the-world airplane for Steve Fossett (man, that guy has some great toys!). If successful, SpaceShipOne might break the X-15's altitude record, but perhaps not. SpaceShipOne is designed to go at least 100 kilometers high, the X-15 record stands at about 107 kilometers. However, it won't go faster than the X-15. In fact, it'll only go about half as fast. From the Scaled Composite website:

Our plan involves flight in a 3-place spaceship, initially attached to a turbojet launch aircraft while climbing for an hour to 50,000 feet, above 85% of the atmosphere. The spaceship then drops into gliding flight and fires its rocket motor while climbing steeply for more than a minute, reaching a speed of 2,500 mph. The ship coasts up to 100 km (62 miles) altitude, then falls back into the atmosphere.

From this source:

Power Source: One (1) Reaction Motors (Thiokol) XLR99-RM-2 throttleable liquid fuel (liquid hydrogen, anhydrous ammonia) rocket. 57,000 lb (25,855 kg) thrust. (First flights were made with two (2) Reaction Motors LR11-RM-5 engines at 8,000 lb (3,630 kg) thrust each.)
Wing Span: 22 ft (6.7 m)
Length: 52 ft, 5 in (15.98 m)
Weight: Approx. 14,000 lbs (dry); 34,000 lbs (fueled)
Maximum Achieved Speed: 4,534mph (Mach 6.72)
Maximum Achieved Altitude: 354,200 ft. (67.08 miles)

There's a lot of good X-15 data at this source.

So, what does Rutan have in mind for a follow-on to SpaceShipOne? Well, it seems he's involved in DARPA's RASCAL project. Here's some more info on RASCAL, although it may be out of date. The mothership portion that Rutan is supposed to be building is designed to exceed Mach 3 and 100,000 feet - which is about as fast and higher than the SR-71 flew. Not too shabby for a guy who made his name designing homebuilt aircraft.

BTW: I didn't get to make it to the new air museum when I was in DC last week. It closes at 5:30 PM every day and I just couldn't get there in time. I did spend a couple hours on the Wright Brothers anniversary at the old NASM. There's a fair chance that I may be going back to DC sometime in February or March. If so, I'll try again.