The P-72 would get my nod just on the batteries alone. I own a S100 Digital Elph and it's been a fine camera to always have with me. It's the size of a credit card, metal bodied and performed just fine.
But the battery was always bugging me. I could drain two batteries and not take the 100 pictures that could fit on the 128MB memory card. Times have changed and I resisted replacing it for quite some time. Then I happened on a deal on a refurb'd HP-812 and while its not as small as the S100, the batteries are lasting a long time, the features are beyond what the (now old tech?) S100 has and I paid a fraction of what the S100 was.
AA batteries are a great solution for this class of camera.
What is Digital Elph on the canon cameras?
I'm deciding between:
SD100 Digital Elph
S230 Digital Elph