Since the video quality between the Panasonic Lumix TS1 or Kodak Playsport look similar, I'd suggest making your choice based on whether you want higher quality still photos or not.
For 12MP photos, go with the Lumix TS1 digital camera -http://www.amazon.com/gp/product/B001QFZMB0?ie=UTF8&tag=amazo09-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=B001QFZMB0
For 5MP photos an a mini camcorder (focussed on video) go with the Playsport - http://www.amazon.com/gp/product/B0032Z73B4?ie=UTF8&tag=amazo09-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=B0032Z73B4
Since you mentioned underwater shooting, I think you can get what you need with one of the above options. In your case, I'd forget the Kodak Zi8 unless you want to forgo the underwater option.
Well I'm deciding between the Panasonic Lumix TS1, Kodak Playsport and Kodak Zi8.
I travel frequently and so video is a must, but I like taking pictures also.
Underwater video is a plus, but if it's sacrificed for video quality it's okay if it doesn't have it (zi.