First, try everything on a shakedown. I tried a lightweight, compact camera on a shakedown and was really disappointed in the slow focusing and poor picture quality in low light. It was a good point-and-shoot for the time, a Canon SX110 IS, but it wasn't even close to my DSLR. Those cameras have tiny silicon sensors which have really high noise in low light. There isn't any way to fix that but get a bigger sensor, which means bigger glass, bigger motors, and bigger batteries.
I insist on keeping my camera ready, but on another shakedown, I learned that having a camera around your neck and shoulder for two days hurt my neck (throughout the third day of hiking).
I took my Canon EOS 50D with an EF 17-55/2.8 to Philmont. It was the heaviest single thing in my pack, but it was worth it. In fact, at 4+ pounds, it was double the weight of my pack, tent, or sleeping bag.
I used #5 S-biners to clip the camera strap to the straps that go between the backpack stays and the shoulder straps (Six Moon Designs Starlite). This is clumsy to get on and off, but good while you are hiking. When I needed to clip the camera back in, I asked another crew member to do it. There was always someone with their pack on first.
I made a "camera poncho" from silnylon with velcro dots glued on the edges. We didn't get much rain, so I did not give that a full test.
I did bring a second battery and used it. If I remember correctly, I swapped batteries on day seven. I brought a charger, thinking I might be able to beg some juice at a staffed camp, but I didn't use it. A lot of staffed camps are all-solar now, so they doubt they have spare electrons. I probably could have recharged at Cimmaroncito, I think they have power lines. I did use the charger to top off the batteries at base camp before the trek.
I have an 8Gbyte card and that was a little tight at Philmont. Next time, I'd go up a couple of steps, probably a 32 GB.
Here I am with the camera poncho deployed at Abreu. My son took the point-and-shoot, this was taken with that camera (duh).
Finally, here is a set of Philmont photos edited down from what I and my son took with the two cameras. Towards the end, there are some photos of the bear we saw. These are extreme crops -- I also included the full frame. I don't think I would have any of those photos with a slow-shooting point-and-shoot with a tiny, noisy sensor. To find the bear photos, look after the Mt. Phillips sunsets and before the rock climbing.
Flickr set: Troop 14 at Philmont
For comparison, here are the photos with the point-and-shoot from a three-day, 32 mile hike. There are many fewer photos per day than there were from Philmont because I threw out so man as unusable.
Flickr set: Troop 14 hikes Skyline to the Sea