For a skilled rider in reasonable terrain, the efficiency of a unicyle is not that different from a bike, and drastically higher than walking.
The bicycle is popularly regarded as the most efficient means of human powered transit. Basically you sit there, use a smooth rotational movement, and mechanical advantage sends you sailing easily along, wasting no effort in vertical movement or pavement impact. As speeds increase, the largest energy expenditure on a bike rapidly becomes fighting air resistance, which is why drafting is a thing.
For a skilled rider, a large wheel unicycle is not very different from riding a bike. Yes, there is a foward and backward component to balance, but just as in the skill of walking, this is not done by loosing control and then recovering it, but rather by adaptively putting just a tiny bit more or less effort into the pedals - effort that all contributes to useful progress over the ground anyway. In fact, if a unicyclist does actually start to fall over (essentially always falling forward) the "save" is a mad burst of pedaling - effort expended at an inefficient rate, but still ultimately going towards covering ground.
Typical cruising speed when riding the largest current production pneumatic tire (36 inch) direct drive is around 16-20 km/hr. If one were to equip a cruiser bike with the same low gearing and short cranks, the efficiency would be effectively the same. Put the ordinary sprockets back on the bike, and now a bicyclist riding alongside the unicyclist at the same pace can pedal more slowly and gain a small advantage there, but the actual power output to roll the same speed will be about the same. The thing is, a bicyclist of comparable enthusiasm to someone able to ride a unicycle smoothly is probably not going to be content to roll along at 20 km/hr, but rather will go a bit faster. However, this does not make them more efficient - actually the opposite. Because energy expended fighting air resistance increases rapidly with speed and overwhelmingly dominates at higher cycling speeds, the reality is that someone rolling along at an easy pace on a unicycle is actually moving more efficiently than the person who passes them going twice as fast on a road bike. A bicyclist going just a little bit faster could be more efficient that the best unicyclist, but the bicyclist would have to chose to actually ride at their most efficient speed, rather than be guided by more typical desires to get somewhere or get in a workout before they get tired of the saddle.
To look at some specific situations:
What about coasting? While exceptions exist, unicycles are conventionally fixed gear. However, "following through" while the wheel moves the rider's legs requires little effort. There's probably a small loss of efficiency compared to a bike in terrain of gradual 1% up and down. Really though the main issue with being unable to coast is being unable to simply stand out of the saddle to get a break from its pressure - it is possible to stand for a half minute while pedaling (much easier if a narrow handlebar is fitted) but it requires quite a bit more work than to stand while coasting.
What about climbing? To some extent, the "gearing" of a unicycle is already optimized for gentle climbs, so that's a place we often pass casual bicyclists. Steeper hills can become a challenge leading to a decision to walk instead. It's not that the unicycle is less efficient than walking, but rather that one may simply not have the power output available to climb at the roughly 9 km/hr below which it becomes a challenge to keep a unicycle stable, but be quite able to hike up the incline at 3-4 km/hr on foot.
Descending hills. For moderate descents work can be done to resist the wheel, but a brake can also be fitted. I had an extended descent the other day where I actually had to take a rest break - not for my legs, but because my brake hand was getting tired.
What about obstacles? Reasonable dirt and gravel surfaces, etc are readily covered on a unicycle, and there is a whole discipline of mountain unicycling devoted to tackling technical mountain bike trails, "trials" involving vertical bunny hops onto stack of shipping pallets or stair railings, etc. Often the appeal here is the challenge not the efficiency, though for things not beyond the unicyclist's capability something like a fire road would be more efficiently ridden than hiked. And switching between riding and walking can be a great way to cover ground as each provides some break from the particular fatigues of the other.
Stop and go traffic, tight turns. To someone who can idle (trackstand) on a unicycle, this may not be a big deal; to others, constantly stopping and remounting could indeed be an efficiency loss. I might chose to walk rather than ride a neighborhood trip if I knew I'd have to stop three times in a mile, but the reality is every time I do, the first time someone passes on a bike I realize that even with this annoyance, it would have been faster and more efficient to ride my unicycle.
Carrying things. I've done meaningful grocery shopping 8 km away using a backpack and a unicycle, but realistically for short distances one can carry more on foot, and for long ones bicycle panniers or even a trailer are going to have more capacity and exert less toll on the body.
One should be careful of mistaking things like endurance or range for efficiency, but there are of course some relationships. A bicyclist may often be able to readily access their entire ability to output energy over a day. In contrast, someone hiking may experience fatigue, but may find their range more limited by things like impact stress. Riding a unicycle tends to fall somewhere in between. Riding smoothly presents almost no impact stress, though jumping on and off frequently definitely can. Saddles tend to be larger than those on a bike, and out of saddle breaks more limited, so saddle-related fatigue can be more of an issue, particularly for a developing rider (a chamois and anti-friction cream are definitely recommended, along with a handlebar with permits a more bike-like limitation of saddle contact to sit bone pressure and not thigh control).
Ultimately an only moderately-active individual who invests effort in learning to ride smoothly, remount without support, and climb moderate hills can probably do dawn-to-dusk "Century" (100 mile or 160 km) rides, while likely challenged to hike even a third that far. Experience doing these confirms that rolling along spinning high cadence into negligible resistance is a moderately low effort way to spend an "active" day. Someone on a bike might get it done in half the time, but at the actual expenditure of more energy.
