Maybe. Consider that humans are constructed to replicate themselves. But our ability to repair ourselves is rather limited. Being able to replicate does not imply the ability to completely self-repair. Being built to mine asteroids and manufacture a new probe doesn't imply the ability to disassemble one's self and replace parts.
Well not so much constructed to replicate themselves as randomly evolved to produce offspring. Many of the limitations on human self-repair ability are down to accidents of ontogeny which are pretty irrelevant to a robot probe. It's easy to imagine a modular machine that can easily replace a defective limb or brain by simply plugging in a new one. That's a lot harder to do with a lifeform!
Oh, and I was talking about a probe with a bunch of Von Neumann machines in it. If each can make replacement parts or entire new machines from materials mined from an asteroid, it ought to be able to do the same from the materials of one of its companions that's broken down. Presumably there'll be some wastage and energy loss involved in the process, but it would hopefully extend the probe's useful lifespan far beyond a machine incapable of self-repair. The probe could carry spare fabrication material of course, but it'd be logistically simpler to have it pre-formed into useful components like parts of the Von Neumann machines, so you might as well put those parts together into functional machines in case the probe needs their processing abilities.
Well, the crew comes with a bunch of self-repair that you don't have to do any design work to get, and medical capabilities to cover much of the rest. More important to Tom's point, the crew can come up with entirely new solutions to problems in-flight.
In effect, building a von Neumann probe to do all this requires reinventing many wheels already developed for humans - mostly in terms of intelligence and adaptability. Right now, we find exploration to be more efficient with probes, but those probes do *not* have all the abilities of a human laboratory. They are far cheaper than sending humans specifically due to their limited capacities. When you may actually need the full capabilities of lab and factory, the probe may not be the most efficient route. Machines are great for specialized tasks, but maybe not for generalized goals.
The "If for some reason a living crew is just as efficient as a robot one" includes the assumption that the robots have some kind of AI or expert system that perform roughly par to humans, at least as far as whatever task the interstellar vessel's designers sent it out to the stars to perform.
The details of said performance may be very different, of course. The human crew might solve problems with the ingenuity of their soggy brains which the robots avoid by meticulous error-checking or by computer modelling myriads of responses to an approaching threat to try to guess which is more likely to succeed.
Or, the ship can use a combination of the two. A generation ship full of humans might have self-repairing systems that require minimum maintenance. A crew of robots might fly an interstellar colony ship through space for centuries, then defrost the human crew to do the tricky work of figuring out surprises and supervise the womb-banks to produce the colony's "first generation".
Since we don't know the technical feasibility or difficulty of either approach, it seems premature to assume which one is more difficult. A human generation ship would have to be enormous compared to a robot probe. If it uses up the resources to build a thousand robot probes but is only ten times more likely to produce the results you want, there'd be little point sending one. Contrariwise, if the ship's task is something only humans can do (abstract thinking beyond the future robot's AI, breeding little humans, or whatever), you'd have to send the generation ship.
