I took the LPI exams a few months ago and I'm signed up to take the RHCE on 8/22/03. The RHCE is the toughest Linux exam out there and is the only Linux certification that is a performance based lab, rather than a written exam.
I don't know if either are "in demand", but attaining the RHCE certification definitely proves to employers that you know your stuff when it comes to Linux (specifically Red Hat). There's no such thing as a "paper RHCE" as you can't cheat your way through a lab, unlike M$'s MCSE and other certifications.
If you want to get a Linux certification, start with the LPI level one exams. CompTIA's Linux+ exam is a waste of time IMO. The Linux questions on the Linux+ exam are very basic while the hardest questions on the test were general hardware questions that had nothing to do with Linux. The LPIC-1 objectives are basically the prerequisites for the RHCE RH300 class. The LPI 101 and 102 exams were actually much harder than I expected, and were definitely tougher than any Microsoft, Novell, Cisco, or CompTIA exam I ever faced. The questions were fair, however, so if you know all of the material listed in the objectives, you'll be okay.
For anyone who wants to take the RHCE, I would recommend taking the LPI 101 and 102 exams first. Passing these exams probably means your ready to start studying for the RHCE and Red Hat's RH300 course (if needed).
ChrisP