they work using different principles. LC-DCP achieve fixation by friction between the plate and the bone. Compression can be applied with an articulated tensioner or using eccentric screw placement in the holes. LCP plates with locking screws are a fixed angle construct, kind of like a bunch of mini blade plates. It is also called an "internal fixator" since the mechanics are similar to a ex-fix. It does not rely on friction b/t the plate and bone so it does not have to be directly on the bone (hence the ease of sliding it up a submuscular, (vs subperiosteal) plane.
Another difference is cost, especially the screws.
Say you have a non/minimally comminuted both bone forearm fx. using locking plates does not add much except cost. Now, bridging a large area of comminution or in people with osteoporotic bone is another story. There is a good JAAOS article recently talking about locked plating.