what is the difference between these two prepositions

There's no difference in meaning of which i am aware. Jumping over the fence would probably the more commonly used locution, but either one expresses the same idea.

The phrase 'Jumping across the fence' is not likely to be used, though it's not grammatically incorrect to my knowledge. It's an awkward expression.

It is more common to say 'jumping over the fence'.

You can jump a fence, or jump over a fence.

You jump across a ditch.

I suppose, speaking generally, "across" signifies a length (or width), and "over" signifies a height.

Even completely nonsensical English can be fully grammatical, Bubu.

McTag has described this, as is his manner, beautifully. So, if he doesn`t mind, I`ll use his words to expand on a few ideas. (deep bow)

You can jump a fence, or jump over a fence.

Perhaps because this is a relatively common action, over or no over works. It doesn`t with the same meaning, with, say, a policeman, a car, or for a cow doing its jumping with the moon.

You jump across a ditch.

I suppose, speaking generally, "across" signifies a length (or width), and "over" signifies a height.

Right, so (no, not Joe`s so) what comes to mind when across the fence is used is a fence lying on the ground or a steeplechase rider standing on the horse`s back, already above the fence and jumping across the top of a widened steeplechase obstacle.

As McTag has explained, that`s the feel of the word across. There may be situations where it isn`t always so (not Joe`s so either).

That would be my take on it, "Across" something usually indicates a horizontal distance of some sort while "over" indicates a height.