They also have issues meeting emissions targets - both because of the basic design (there isn't the ability to actively control valve timing events), and also because they typically need some sort of lubrication for the combustion chamber. They are similar to two-stroke engines in these respects.
Running them at a pre-determined RPM constantly can resolve lack of VVT, but that limits their applications. New materials for apex seals being researched could alleviate their longevity issues too. But, I have a big soft spot for rotaries and would love to see them applied more :(
I think it's difficult to make a direct comparison because of the way the capacity of the engines is calculated. I know it's "fair" from one point of view, but it's not from another (depending on which team you support).
The only straight-ish comparison I can think of is the Suzuki RE5 vs the GT500, which are same-era motorbikes from the same manufacturer, with roughly the same capacity. The RE5 wins on horsepower (62 vs 44), but weighs about 50kg more.
