Of the two, Fringe is the more direct descendant of The X-Files, and not only because it's on Fox, although that might have something to do with it. In fact, the FBI characters on Fringe have referenced "the old X designation" (Mulder and Scully's little department, which was shut down) and which has now been replaced by The Fringe Division. Like their predecessors, FBI agents Olivia Dunham and Peter Bishop (not officially and agent, but he might as well be) encounter shape-shifters, weird creatures and possibly beings from another universe. The show's tone and themes are very similar to The X-Files, and it approaches its paranormal subjects with the same proper amounts of intelligence and humor.
Warehouse 13 isn't quite as serious a show, but it has a very interesting premise. If you'll recall the ending of Raiders of the Lost Ark, the powerful Ark of the Covenant was crated up and stored in a vast government warehouse. Warehouse 13 is one such warehouse, located somewhere in South Dakota, and it's packed with all manner of artifacts from all over the world that have supernatural powers or properties. The two agents here are Warehouse Agents, and it's their task to trot the globe in search of these artifacts before they cause trouble or get into the wrong hands -- and, of course, they often do. Although its cutsie humor can get annoying at times, the show's saving graces are its imaginative artifacts (Edgar Allan Poe's book and quill pen, for example) and retro steampunk warehouse and gadgetry designs.
As of this writing, Fringe is beginning its second season and Warehouse 13 is well into its first season. I recommend them both as enjoyable, paranormal-themed entertainment.
