The areas Wi-Fi Direct can best Bluetooth are on distance and speed: I've written a few articles already about Wi-Fi Direct, the new peer-to-peer mode that the Wi-Fi Alliance is finalizing and which will appear in updated and new hardware in mid-2010. This includes my analysis of why Bluetooth and Wi-Fi Direct serve related but not entirely overlapping purposes. But in that discussion, I only mentioned speed and distance in passing.
Bluetooth devices come in one of three varieties by signal output: Class 1, 2, or 3. Class 3 devices (1 meter, 1mW) were originally the most common, intended for low-power earpiece-to-phone communication. Class 2 (10 meters, 2.5 mW) became more common, and I believe now predominates. This allows communication within a room and sometimes beyond. Class 1 (100 meters, 100 mW) is rarely found in peripherals, although it's used in computers. The Callpod Dragon V2 headset ($99) is a rare peripheral exception, but the size and price have something to do with its ability to push out that much signal.
Wi-Fi, in contrast, is designed for whole home/whole office coverage, with 802.11n finally achieving that for many venues. Wi-Fi equipment makers used to, and some still do, put out nominal distance numbers, like 100 meters diameter or what have you, but I always thought these numbers were nonsense. Originally, these distances were based on minimal testing in simulations of the real world. Some companies and trade groups have houses that are designed to be testbeds, even.
In practice, 802.11g Wi-Fi was a one to two wall and one, maybe two floor solution. A lot of factors about building materials affected that. 802.11n penetrates far better, and can produce a far clearer signal (and thus higher speeds) through many more obstructions.
For Wi-Fi Direct, where you want to be able to peer easily to devices around you without fuss, the distance and penetration issues may be one important component of why people may turn to use that mode rather than Bluetooth. It's possible that some operating system makers or third-party software developers will make it simple for Wi-Fi Direct to become an ad hoc Internet access mode, bypassing the need for guest networks in access points, for instance.
Speed will also be a component depending on the uses to which Wi-Fi Direct is put, and how OS makers and device makers incorporate the mode. If Apple lets me use Wi-Fi Direct on an iPhone to transfer data from an Apple TV or a Mac or Windows system with iTunes installed (say, as an extension of the firm's new Home Sharing feature in iTunes), then I will surely want the 50 to 150 Mbps available with Wi-Fi Direct instead of the 2 Mbps of throughput from Bluetooth 2.1+EDR.
This draws me back to the application and profile issue I discussed in the previous article on Bluetooth competition. The usage Wi-Fi Direct beyond simple file transfer and Internet access and printing will depend heavily on having layers of functionality (tasks and purposes) put on top of connectivity.