Have both of these computers, as well as the older Pursuit hardwired to my Megalodon CCR.
Predator screen is a little easier to read in bright light. Petrel is still very good. Both are much better than Pursuit with backlight and mono LCD display.
Petrel software is a bit better - new gas change system, centre line display options, and tissue graph are good improvements, but I understand the next Predator update will include these features.
The Petrel is a bit smaller than the Predator. The size was the only thing that I did not like about the Predator. The size difference is a definite improvement but probably not enough to make the Petrel a clear winner. If you are diving a drysuit or are not a small diver then it is even less of an issue. IN the ropics and with a thin wetsuit or a dive skin, the Predator seems like a bit of a brick out of the water, but is OK once submerged.
The Petrel takes just about any AA size battery and seems to have an improved battery meter. I found that with my Predator the only way to get reliable consistent battery power that did not result in regular (mostly) false low battery warnings was to stop using the recomended Saft batteries and use a recharcheable Aw Lithium battery.
Both are excellent computers, especially for more advanced/technical diving, and have a very intuitive menue system. They have the best factory back up of any dive gear I am aware of. I would recommend the Petrel because of its better battery options and smaller size, and lower initial cost, but a second hand Predator at the right price would also be an excellent computer.