Some other things I'd add to Gilligan's list:
- Size of the camera, do you want something that'll fit in your BC pocket or do you not mind? The P-10 will fit nicely in a BC, some of the Olympus cameras will too but not the more popular 5050 or 5060....not unless you have very big BC pockets
- Functionality of the camera. Do you want a point and click type camera or one where you get to do more adjusting - being able to adjust aperture, speed and white balance can be very useful underwater. The Sony P-10 does not allow a lot of adjusting
- Proprietary accessories - Sony cameras fairly much only use Sony cards and accessories, the Olympus cameras are a little more flexible in this regard which can reduce your costs a little.
On a personal note I've used the Sony P-8 and now own an Olympus 5060. While I was happy with the P-8 I'm even more happy with the 5060. The 5060 gives me more flexibility, the colours seem better, I can have more storage media in the camera and the marine casing is cheaper - I discovered after the lens of the marine case leaked that the Sony guarantee doesn't include the casing so it can be costly if you have to replace it. As that was the second problem I'd had with it I didn't replace it, I bought the Olympus instead and haven't looked back since