I think incontinence feels different for most people.
In my case it is a result of a motorcycle accident and I have what is called nuerogenic bladder and partial bowel, and that means I dribble urine with no sensation that I am leaking at all. Depending on how much I drink depends on how much/fast I leak. I think it is really wierd, because no matter how much I squeeze my muscles it has no affect on my leakage.
As far as how it feels well, it feels like nothing. Except for making sure I monitor how damp my diaper is, there isn't much else to it. Now when I was told I had to wear diapers (at the age of 27) I was both mad, and extremely embarrassed, that was until I had my first accident in public, then I couldn't be caught without wearing one.
It was simple with me, I am more affraid of having another accident, then I am of wearing a diaper.