The only reason I got into cycling is because I'm handicapped with a very messed up lower back. I had to quit jogging 21 years ago because of it. Walking, standing and even sitting up straight cause pain. I can ride a bike because I'm bent forward at the waist and that takes the pressure off my back. Even when taking a shower, by the time I wash my face and hair my right leg has gone numb. I mostly sit through a shower anymore as it's just not pleasant to stand that long.
Yes, I've seen a couple of different specialists. My current specialist is a neurosurgeon who will fuse some of my lumbar discs together if I can lose some weight. He's already performed carpal tunnel surgery on both hands and the result has been fabulous.
I enjoy cycling immensely, however, given the choice of cycling vs. jogging, I'd take jogging. No question about it. I believe it's much safer too as it's easier to get away from cars. There are way too many idiots driving.