the question is if the stability issues are due to the driver, or due to the driver's interaction with the rest of the kernel.
Personally, I suspect that most of the problems are in the latter category.
The closed driver is having to interact in a multi-threaded environment with other processes manipulating memory, with allocating memory in the same space as the rest of the kernel, and with all the locking that the rest of the kernel expects (and in some cases requires). And the closed driver is trying to do this without being modified from kernel version to kernel version, even though the rules for the kernel are changing (the locking rules in particular, although memory management changes somewhat as well).
If stuff running on the GPU limits itself to reading and writing buffers that are explicitly allocated for it, almost all of the problems mentioned go away, and the remaining 'shim' driver can evolve along with the rest of the kernel.
In this case, they talked about how part of the difference was the closed drivers supporting a newer version of opengl, with the high level interface this would not vary from driver to driver (unless specific drivers required different versions of the firmware), so I would expect that things would be a lot closer to feature parity between the two modes.
In any case, even with the ATI mode of doing things, if there is bugginess in the firmware, it can cause problems for the overall system