What would a sufficiently dense sphere of uranium do first: blow up, or form a black hole? I think it is safe to assume that humans are a long way off from having either the technology to compress a normal-sized sphere of uranium below its Schwarzschild radius, or the technology to create a sphere of uranium with a mass comparable to that of a star, so this is deep into idle-curiosity-land, but supposing that we "called into existence" a sphere of uranium whose mass and density was sufficient for both the effects of nuclear fission and gravitational collapse to be relevant,

does the sphere of uranium explode due to nuclear fission, or collapse into a black hole, first?

Of course, perhaps there is a combination of effects - maybe the sphere starts to undergo fission, but forms a black hole before any explosion can take place.
 A: I think it would be very hard to provide a rigorous answer to your question, but i can think of hand waving arguments suggesting it would do both. The outer portion of the sphere would explode while the centre would form a black hole.
My argument is that the mass of uranium required to form a black hole is around the same as the mass of a star big enough to form a black hole - give or take a few orders of magnitude. If you could magically conjure into existance a star sized lump of uranium then the neutron capture efficiency for all but the outermost layers would be 100% and the uranium nuclei would all fission within a fairly short time.
Suppose we take our sphere of uranium to have the mass of the Sun, about $2 \times 10^{33}$g, then this is $8.5 \times 10^{30}$ moles of uranium 235 or $5.1 \times 10^{54}$ atoms. Fission of $^{235}$U releases $3.2 \times 10^{-11}$J per nucleus, so the total energy released would be $1.6 \times 10^{44}$ joules. This is remarkably close to the energy released by a supernova, which is in the range $10^{44}$ to $10^{46}$J.
So the fissioning of the uranium would produce something very like a supernova, and we know that supernova can form black holes because the centre is compressed by the explosion. Whether this would happen with the uranium sphere is anyone's guess, because of course the details of the explosion would be quite different in the two cases. However I think there is a sporting chance that, like a supernova, you could end up with most of the sphere being blown away but a black hole remnant remaining.
