I'd get the model with the most manual controls. My other criteria is that the camera is sturdy and built well, because my point and shoot is a "take anywhere" camera that will be at the beach, in pubs, parties, etc.
Why these 2 things? Because I think they're both going to be approximately the same in terms of photo quality, so things like manual features, easy to use interface (menus, etc) will make the difference.
Oh, and since I went to that Kodak website you linked to in order to read more about it (
ie: something like this page here), and thought the webpage was a mess, I'd suggest the Olympus first.
I was trying to find out more details about the dual lens technology they use, and found a link at the bottom of the "V570 Imaging Technology" webpage that links to another page not listed to the side. If their UI is as messy as their website, I'd go crazy and wouldn't bother.