Kay, I usually travel with both a compact P&S Camera and a dSLR with assorted Lenses and other kit. While the dSLR is a LOT more trouble to pack around, it provides the capability to get photos in some challenging condtions (ie: low light or at night, etc.). Having a range of controls to work with (ISO range, shutter speed and aperture) makes a big difference!
My philosophy is that if I'm spending a small fortune to travel to a particular location (one that I might never return to), I want some good photos to remember the experience!
Using only a small P&S Camera will probably minimize the risk of theft slightly, but I'm sure the petty thieves are aware that virtually ALL tourists will have a Camera with them. If the Camera is in a pocket, it might be even easier for them to steal than one that's being held?
I haven't had any theft problems so far, but always try to be vigilant.
Good luck and happy travels!