What is the difference between the prednisone pills and the shot and which is better and how long?

I suppose it's what you are taking it for. If it's for specific area inflammation, I think the shot would be better. I've never done this, but I think getting the medication specifically where it needs to be is good.

I take it for auto-immune disease flare ups so I have the choice if pills it an infusion. I've done both and find the infusion literally leaves me with a bad taste in my mouth for days, so I prefer the pills. They also taste bad, but only for the amount if time it's in your mouth (I recommend having something flavorful afterwards, like juice, to wash the nasty flavor away).

The main difference is the shot stays mainly in the area it is given such as the knee. Some of it will be systemicly absorbed throughout the body. The shots are supposed to last 2 to 4 months. Taken orally the medicine is metabolized by the liver and goes thru the entire body which if taken for a prolonged period of time can cause brittle bones, unwanted body hair. A syndrome called moonface, the list of side effects for the oral type is quite long. The injections are safer in the long run. Best of luck to you.
Packard2046