I'm not a pilot, so take everything I say with a grain of salt.

Yes, a mistake can lead to a go-around, which at a busy airport can easily add an extra 10 to 20 minutes of flight time. But as long as no such mistake is made, a hand-flown visual approach can actually be quite a lot faster.

But first, we have to clarify the terminology. On most instrument approaches, the autopilot only flies the beginning of the approach, until the pilot flying decides to disconnect and lands the plane manually (somewhere between the final approach fix and minimums, depends on visibility and crew preference). So the most common way of flying an approach is neither fully automated nor fully manual.

Autolands are only done rarely, like in low visibility or periodically for pilots and aircraft to stay current. Visual approaches, on the other hand, are more common (though it depends on the region, controllers in the US hand out more visual approach clearances than controllers in Europe for instance). But even on a visual approach, crews often keep the autopilot engaged until very late in the approach or at least use the ILS as an aid while flying manually. That makes it tricky to do a comparison.

All external conditions being equal, I'd assume that an autoland is indeed less likely to lead to a go-around than a hand-flown visual approach. This is mainly because autolands, like other instrument approaches, are typically set up with a long final and earlier stable gate (typically 1000ft). A lot of go-arounds happen due to being unstable at the gate (too high, too fast, not configured, etc.) - that's less likely with an autoland which forces you to be stable much further out. Additionally, an autoland has a very low decision height leading to fewer go-arounds in marginal weather (though in such cases a visual approach most likely wouldn't be attempted in the first place). On the other hand, an autoland has stricter crosswind and maybe also tailwind limits, could be subject to ILS signal interference, and usually requires two or three autopilots to be fully functional. Still, the first argument has more weight to it I think.

But assuming no go-around, a hand-flown visual approach can be quite a lot faster than an autoland! As I already mentioned, autolands need a long final to establish early to give the airplane time to stabilize (often crews are looking to establish well prior to the FAF). A visual approach, on the other hand, allows tight turns onto final, slowing down and configuring the airplane much later, etc. The aircraft needs to be stable at the gate, but when flying visually that's typically 500ft AGL, so short final basically. Visual approaches also give controllers more freedom to give vectors with fewer track miles, and visual separation allows for reduced spacing.

Overall, I think that hand-flown visual approaches often save time compared to autolands, and possibly over other instrument approaches as well. And even if the probability of a go-around is slightly higher (assuming equal weather conditions), a go-around is still so rare that despite being a significant outlier in flight time, I wouldn't think it moves the average up much.

But maybe the comparison just doesn't make much sense to begin with. An airplane is flown by pilots and computer systems together. Pilots can choose between different levels of automation, but both extremes of the automation spectrum (on the one hand: fully hand-flown visual approaches without even the ILS frequency or any navaids tuned in; on the other hand: full CAT III autoland) are quite rare for airliners. Most approaches fall somewhere in the middle on that automation spectrum. Is that the safest and quickest way to do it? I don't know. But I assume the industry has converged on it for good reasons.