L (Death Note) vs Professor James Moriarty

Here's a good match-up I think. Both are genius-level characters, and keep their opponents on their toes. L takes on Prof. Moriarty [classic novel version for the prof.] in Old England, where he has the support of Scotland Yard. L replaces Sherlock Holmes throughout the run of the novels. Can he beat Holmes for sheer efficiency and take down Moriarty before the events of Reinbach Falls?