Just like to say that even though we were with a tour we had lots of spare time to do our own thing, and we did. We saw Petra at our own pace too. The good thing about tours is that you don't have to worry about booking transport and hotels in each place. We covered most of Jordan on our tour, and we often went off on our own. I usually go independently to other places, including Egypt, but found it easier and a lot cheaper actually to go with a group to Jordan, Syria and Lebanon. We felt very safe in all these places, and we also took off on our own in the latter two. I suppose its up to the individual, but if you feel happy going it alone and its actually cheaper then by all means do so.
Did miss out on points at the Crowne Plaza in Petra though!