I was in both places recently - they swap back and forth as to which is my favourite. Camping is easy and safe in both.

The local Jordanians are incredibly friendly and hospitable, but many of the people you encounter (ie people transitting the country in vehicles) are not. You can camp just about anywhere. I was too tired to look for a site or a hotel one night and camped in the carpark of a police station!

Once you get used to the brashness of Israelis you will find them the friendliest people in the world as well (like most countries really). Camping is like in the west - ie a bit more controlled near urban areas but do what you like in the countryside (with the usual manners regarding private property). The only Israelis that gave me a hard time were from the more remote hilltop settlements (well that was only once, but I was checked out a few other times). The Palestinian Nazareth area shouldn't be missed either, but be prepared to be visited by everyone within walking/riding distance (keep a pot of tea on the fire).

Speaking of guns in Israel...I walked out of a pub in Jerusalem one night (that bar area near the YMCA) after 1000 s to see a truly stunning woman in a tight jumpsuit, talking on a mobile and applying lip gloss with her finger. Stopped me in my tracks. I moved on again when I noticed a rifle over her shoulder. She was an on-duty soldier! I did think of doing a lap of the block to get another glimpse of that armed goddess but sensibly thought better of it.

cheers
Brett