Rhone,
To address your question with a few numbers.
The database I've been compiling has approx 165 deaths when the diver was using or had been on a rebreather. With my first case in the early 1950's.
There have been over 600 deaths while Cave diving most of them on OC.
Also when tracking the deaths, causes on a timeline relative to training and new technology (ADVs were a big improvement) different looks and perceptions of the data are seen.
I don't track OC related deaths, but its safe to say that its a fair number and I think its safe to say there have been over 1000 since the same time frame.
Now like any statistic you have to use some sort of reference. If you take all RB divers / RB deaths and compare it to all OC divers / OC deaths then compare those two fractions one could state that RB deaths are more. But lets take a look at the OC diver base. If agencies are to be believed, then about 80% of all OC divers are "vacation" divers. Go on semi-guided tours with DMs and other lower risk type dives. But as pointed out by GillEnvy, most RB divers are doing deeper, longer dives hence higher risk environments. If your OC data set is reduced to get a more matched set of diver profiles the difference in statistical danger may be considerably less. One of the problems with these statistics is that determining the base of users is very hard especially for RBs. A few folks have tried using various methods to try to come up with a baseline of users, but at best is still an estimate/guess.
Are there a significantly higer number of people diving RBs then diving Caves? (yes there many who do both, but RB deaths in caves is still very low). Looking at that set of numbers you may note that OC diving in a risker environment (caves, wrecks etc) may be more dangerous then on an RB. But without base numbers everything is just a guess/perception.
As pointed out by several folks, RBs are not for everyone, they do not tolerate the abuse and casual care that modern OC gear can. The current state of the art of RBs is still evolving. The constant flow orifice and the training done for mCCRs does indeed appear to challenge the eCCR when looking at just the death rate. There are now two manufacturers that offer a combined system and the technology continues to evolve.
But as so well said by SFLdiver many of us think that RB diving is actually safer then OC diving when in these risker environments, or that the benefits out weigh the risks.
Being wary is a good thing when considering an RB.
All that said, I still prefer diving an RB then OC for most any dive.