Unfortunately, it's hearsay to me; it came up in conversation (about computability and complexity) with a professor, and I took his word for it at the time; I've been meaning to ask him for a reference ever since, but never got around to it.
But at least one thing I can see is that in PR, you need to fix the upper bounds of the loops (/recursion depth) ahead of time, not "on the fly". If you're doing some kind of iterative approximation, you probably don't know what those bounds "should" be, because you're going to terminate on some other condition, like, the change in the value has become negligible. Your upper bound will be a worst-case estimate -- which you have to do extra work to compute -- and I don't see how it differs much, in practice, from a timeout, which has the advantage (again from a systems perspective) of being measured in clock time rather than cycles.
Not sure about parallelization. PR doesn't suggest any advantages to me for that offhand, but then, I haven't thought about it.