Unfortunately, JPS requires a regular grid. And "JPS+" as described here requires (a lot of) computation, which means that it's not directly comparable with A*. (Once you start allowing precomputation, a) it is not longer usable with changing terrain, and b) you have to compete with "precompute all possible shortest paths and store them" (O(1) lookups!).)
Now what I'd like to see is someone coming up with pathfinding that works decently with obstacles being arbitrary polygons. Vector-based as opposed to raster-based.