Jordan is completely safe. I wouldn't be going to Israel right now. When I return I'd like to go to Syria too, especially to see the magnificent crusader castle the Krak des Chevaliers, but sadly that possibility looks like it's a very long way off.
Re. SmartTraveller, Jordan is "exercise a high degree of caution", which is the same as the UK, France and Germany, so basically meaningless. We'd be at the same level; on the Global Terrorism Index Australia is twenty places worse than Jordan.
Saddam still pretty popular - strong nationalist secular Arab leader - and appears on a lot of bumper stickers, but ISIS & their successors are loathed in Jordan.
Israel is "reconsider your need to travel" which will likely invalidate your travel insurance, it would mine with SCTI.
