I think it can be close between a bike and unicycle.
Bike: At least around 2% drivetrain loss? (exclude tires, assume equal for unicycle and bike).
Here’s an idea to calculate effort required to balance a unicycle:
Going uphill for me, I don’t believe I push backwards more than normal(biking) to balance, it’s just pushing forward more or less.
Thus, my model for balancing is pushing 0-10% more on some pedal strokes, and 0-10% less on other pedal strokes. This makes it approximately up to 1.5% more difficult. (explanation in next paragraph)
For example, instead of riding at 200W smoothly (ie on a bike), you ride at 220W for a few pedal strokes, and 180W for the next few pedal strokes. This is harder than just riding at 200W continuously. Bicyclists sometimes use “normalized power” to describe this. If you average 200W, and never go above 220W or below 180W, normalized power maxes out at around 203W. So it is 1.5% more difficult. This is worst case though… if it’s just 220W for a few seconds, followed by 180W for a few seconds, repeatedly, it’s more like 201W normalized power (0.5% more difficult). Normalized power obviously isn’t perfect, it’s just some equations people thought up of, but it works well enough for bicyclists to gauge their effort.
I think a proficient unicyclist corrects with less than +/-10% variations for a smooth uphill road, so from this point of view, balancing effort could be less than 0.5%.
Obviously, if the correction happens by pushing backwards more, versus just letting up a bit, then it could be be wasting a lot more. With 10% variation, that could be as much as, 10% to pedal harder, then 10% pushing backward, resulting in 20% extra effort. However, I rode Diablo with a powermeter pedals before on both unicycle and bike, and my torque effectiveness was in a similar range as when I bike. So I think my assumption that balancing comes from pedal forward more or less could be true.
As gizmoduck said, with the wrong gradient and thus non-ideal cadence, this easily goes out the window.