On Moussaoui, the alleged 20th hijacker, it was the French who provided the FBI field office in Minnesota with information that he was known to them as having associated with terrorist groups. Unfortunately, the FBI counterterrorism office in Washington discounted the French information and no court order authorizing a search of Moussaoui's laptop computer was sought (until after September 11).
As it was, apparently nothing was found on the laptop that would directly support the allegation that he was the 20th hijacker. He wanted to fly 747's, not 757 or 767's. The laptop did contain a good bit of information about crop spraying, and Atta, it turns out, unsuccessfully sought a U.S. government loan to buy a cropdspraying plane supposedly intending to fill every available space with tanks. One can assume that if the US government possessed prima facie evidence that Moussaoui had lived with or even met with any of the 19 hijackers while in the United States, they would not seem so dependent on European records to show his terrorist group associations.
Reid, the shoe bomber, is not a capital case, and there has been no suggesstion that European authorities are not fully cooperating with his prosecution, with the French very recently arresting several suspects who may have helped him.