There is a lot of reference and numbers that tie bicycle riding to energy output or calorie burning on a single. I can't find the same with respect to tandem. Do both riders on a tandem spend same, less - if less, how much less energy to the pedal?

Depends.

Climbing, there are issues with inefficiency if the two have significantly different optimal climbing cadence (and therefore there is no 'perfect' gear). Even if they have similar but different optimal climbing cadence, one will be (typically) expending less than they would on a single, and the other is unlikely to make up for it.

On the level, or a gentle descent [gentle enough that they're still pedalling] the power used per unit speed is normally less, because the wind resistance per rider is lower [only a bit higher than the resistance of the captain alone, in most cases]. Estimates vary, but for reasonably matched [for cadence, not watts per kg] riders, something in the range of 5 to 10% seems normal.

This is assuming both riders are out for a workout when on singles and when on a tandem. I normally put out less energy riding alone on a single as I coast, and let my mind wander. On the tandem my wife doesn't like coasting except for butt breaks and when we top out on downhills. So it only happens at those times and as we approach intersections or tight curves. Very different dynamic.

It varies from team to team, depending on the level of each rider's fitness and contribution of physical effort under different conditions. There are some stokers who are powerhouses who may, in fact, be pushing the captain around. Conversely, there are also stokers who add resistance to the captain's efforts. Only way to know what's happening with your own team is to measure the effort of each rider with a HRM and then plot that data.

Your energy output is really dependent on how hard you are riding. I probably put out less power on the tandem overall, because I get distracted talking to my stoker. I'm more focused on the single.