I have carried a DSLR in a salomon rucksack whilst running but to be fair, it was far too bulky for my liking. I also have a Canon G12 which provides great functionality within a nice compact body. It has produced some great shots and comfortably fits in a bumbag.
Concur with what's been previoulsy said i.e. no GPS device will be 100% accurate Howvere, I have found the TomTom runner to be pretty good as a lightweight running watch. It is usual for it to be a bit short on distance though (and a such means I never get a 5k time for park run as it records it as 4.98k!)
I found having the watch is far more easy to use on the move even though i usually carry a phone in a bum bag anyway.
Check the settings too e.g. Strava can be set to record only when moving so this will affect your pace though obvioulsy not distance.