They are complementary - and are not really alternatives.
The fact that they are complementary doesn't exclude the possibility that one could occur earlier than the other. For example do you think there is negligible chance that genetic engineering or pharmaceuticals could significantly improve human intelligence before machine intelligence gets very far off the ground? Or that roughly baseline humans could create (or stumble onto) a recursively-improving AI?
On the other hand, the "too close to call" case does seem to deserve it's own category, so I've added one. Thanks!
Embryo selection technology already exists, all that's needed is knowledge of the relevant alleles to select for, which should be forthcoming shortly given falling sequencing costs. Within 30 years we should see the first grown-up offspring of such selection. The effect will be greatly amplified if stem cell technology makes it possible to produce viable gametes from stem cells, which the Hinxton report estimates to be within a decade too.
Suppose we could look into the future of our Everett branch and pick out those sub-branches in which humanity and/or human/moral values have survived past the Singularity in some form. What would we see if we then went backwards in time and look at how that happened? Here's an attempt to answer that question, or in other words to enumerate the not completely disastrous Singularity scenarios that seem to have non-negligible probability. Note that the question I'm asking here is distinct from "In what direction should we try to nudge the future?" (which I think logically ought to come second).
Sorry if this is too cryptic or compressed. I'm writing this mostly for my own future reference, but perhaps it could be expanded more if there is interest. And of course I'd welcome any scenarios that may be missing from this list.