The trampoline's advantage is the lack of jarring impact.
A small round fitness trampoline will have an edge effect: Your foot is not in the centre of the trampoline on the bounce, and so there is some sideways torque. If road cambers bother you when running, this may have an effect here.
A larger trampoline doesn't show this effect.
A large decent quality garden trampoline is an excellent workout and a lot of fun. I can max out my heart rate in about 80 seconds. But you aren't jogging on it. You do a bunch of jumps, and turns, land on stomach, hands and knees, back, butt.
If you do this, take lessons before you try flips. Most of the injuries you can do to yourself while being rightside up range from sprains to dislocations to bone breaks if you work at it. Flips can break your neck