You don't detail your actual shooting conditions, which would have been very useful to know. However, in general terms I would clearly prefer the Panasonic TZ-1. I owned both the kodak P850 (which I later old on e-bay)and the TZ-1. The the Z612 is just a newer version having IS in the Kodak Z line.I would suggest that you take a look at and be sure to handle both cameras. The TZ-1 is slightly smaller and slimmer.
Both cameras will do a good job. The Kodak has colors that are a bit more saturated. To give you a sample of classic Kodak colors, I pulled out my older Kodak Z740 and took an inside/no flash photo ofmy husbandas he was napping this afternoon.