With jogging you're pushing your bodyweight against the floor. With ellipticals your pushing against resistance of the machine. If the machine can't match the resistance of bodyweight then it'll take less out of you.
Outdoor jogging has inclines which require you to push yourself against gravity a bit. Declines require you to fight against gravity to maintain balance. Ellipticals don't really have that, though a lot have a sort of "interval" resistance that kind of simulates this. It's not really the same thing.
Jogging provides air resistance which you have to overcome (unless on treadmill). Ellipticals don't have any air resistance at all.
Ellipticals also allow you to use your arms to push against the resistance. So if you have a more developed upper body then you'll be able to last longer. It also allows you to rest your legs a bit if they start feeling tired and vice versa. Jogging is just all legs. If they get tired you'll have to work harder to keep going.
You may also just be more conditioned for ellipticals. They're not the same movements as jogging and running, so it's possible to be better at one over the other.
Which is better depends on what you're trying to accomplish. If you're trying to keep your heartrate up for an extended period of time, then elliptical would be better in your case. It'll burn calories just like any other form of cardio (though ignore the "calories burned" on the machine. It is absolutely wrong). If you're trying to build endurance and stamina, then you will need to push harder and harder, and you'll want to build your jog if you're already reaching the limit of your elliptical.