The A388 will be faster than the 744 but the proposed Advanced model will equal it. http://www.boeing.com/commercial/747family/back/back9.html
Projected economics improvement for the Advanced over the 744 was stated at around 13% overall in a recent FI
article. The gains come from the higher capacity, aerodynamic refinements and mostly, the more efficient 7E7 engines. If Boeing can keep the price reasonable, the Advanced may gain significant orders though I think it'll be a smaller niche than the A388's. The 744 may continue as a freighter only. The A380 doesn't entirely obsolete the 747 if the Advanced model launches and I suspect demand for a 747 Adv. freighter might be robust in coming years. Roberta, the reason many of us don't think the A387 stands a good chance for launch is its' extremely high MTOW compared to the only slightly less capacious 747 Adv. (450 passengers compared to the A387's 481). I've seen MTOW weight quotes for the different 747 models ranging from below 950,000 lb. for the passenger model to between 960,000 to 987,000 lb. for the larger freighter. Compare that with the staggering figure for the A387. "Max Takeoff (A380-700) 1,190,495 lb (540,000 kg)". That's an over 200,000 lb. difference, assuming the figures in this link are correct!
Granted, it has 750 nm more range but I've got to think it would have an impossible task to match the 747 Adv.'s operating economics having to push all that extra weight. As I see it, the 747 Adv. should own the 400-500 pax niche market while, of course, the A388 and A389 rule the over 500 passenger class. Though the 747's design and systems are somewhat dated compared to the A380, performance and operating economics improvements for the Advanced should keep it viable for a couple more decades, anyway.