Goodness, hope Boo doesn't see these answers. Having been a horseback rider for many long years, let me tell you there's no sitting and letting the horse do all the work. You have to balance your weight in the stirrups, hold up your arms so the reins are in the correct position, and keep your back straight. If you post (during the trot), you are raising yourself up and down with the rhythm of the horse's movement. Lots of leg workout also required for guiding the horse correctly. Then there's shifting the weight during different gaits, directions, and terrain. When you coast on your bike, you're still working...right? Well, we're still working all the time, even when it looks like we're not. Trust me, no easy answer to this one. And you could more easily compare mountain biking to jumping the jumps...You know not whereof you speak.
Road cycling is the hardest sport compared to the other one. You need to be very physically fit and have a good lung capacity for the endurance. This is because during cycling you may come across hills and rough roads, which will require you to use extra energy.
Average riding with some jumping... If I add jumping to the mix (20 minutes of walk, trot, canter warm up and 25 minutes of jumping courses) that number goes up to about 750 calories burned. Cycling... Based on the the list of cycling activities, shown below, the average calories burned for an average male, weighing 190 pounds (86 kg) is 707 Calories for one hour of cycling. The average burnt for an average female, weighing 163 pounds (74 kg) is 606 Calories for one hour of cycling.
On both I just posted general calories burned. Eventing is much more difficult, same with road cycling. They are close but equestrian beats out cycling.