Add geospatial to your comparison chart please. The way in which these implement support varies widely in performance and accuracy. I've yet to find one that actually uses R-Trees. Geohashes seem to be all the rage these days.
That's because R-Trees don't scale well with random write loads.
R-tree insertion performance is extremely dependent on insertion order (search for "sort tile recursive"). They're best used for problems where the data can be bulk-loaded and left alone. If random writes are an important part of the problem (as they are for most web-based tools), R-Trees are a bad idea.
That said, they carry a lot of annoying edge cases when determining the adjacency of quadrants, so they're hardly a panacea to geospatial search. Lucene 3 and 4 make a lot of progress in spatial search, but there's still a fair bit of room for improvement.