I own and use a Petrel but willing to talk "nice" about the H3. First, maybe find out if the battery is a special design or an industry standard type. This would mean not only fresh batteries for replacement but possible aftermarket availability even for the manufacturer to source when the need arises. Another item to mention is consider the amount of diving and running time added to the normal drain the batteries will see during the 3 year period you mentioned. If the amount of "full cycles" is low, you should be able to get good life from the batteries. AI is nice to have and less clutter on the wrist and less hoses around the first stage. I personally don't trust it 100% and I'm starting to run a pony and stage bottle from time to time. Form factor can't be beat but honestly, if you are "growing" more into the sport you will appreciate a larger screen and more info. At one time I considered a watch sized wrist computer (Suunto, Mares) but so happy I didn't get one of those. If you normally wear a watch then go ahead and get one because it is no worse than a nice fashion watch and it functions as a full featured dive computer many times better than any Rolex, Citizen or Heuer. I personally have thin wrists and positively hate having anything on my wrist outside of water including a fashion watch, jewelry or charity support band. If you are a wetsuit or drysuit diver, the length of the band may make it wearing out of water clumsy. Lastly, imagine you are diving at night, in low light (happens a lot in the day time) or at an overhang. Do you want a small computer screen or a big one? I personally want a big one.
I agree that more info on the battery would be nice.
My understanding is that all modern Lithium-Ion and Lithium-Polymer batteries degrade over time, whether you're using them or they're sitting on a shelf. Your usage pattern can increase how quickly they degrade, but they're going to degrade no matter what. One article I read said that cell phone batteries can degrade to 50% capacity in 1 year, and even a "good" usage pattern will still generally result in 20% loss of capacity in 1 year. Exactly what that means for the H3 battery? I don't know. More info from the manufacturer would definitely be nice.
I have wireless AI on my Atom computer. I've only got 40 dives on it, over the last 9 months or so, but it has been 100% reliable so far. I don't see any reason the H3 wireless CAN'T be solid. It's just up to SeaBear to give it a good implementation.
As far as the size of it, I want a screen that shows me everything I want to see, big enough to read, but no bigger. Users of the H3 seems to be saying that they can, generally, read it about as well as the Petrel screen - they just don't see as many pieces of info at one time.
I definitely don't care about wearing it out of the water. There are people who wear $10,000 wristwatches. Maybe for them wearing an H3 around would be nothing. For me, an $800 wrist computer is something that would stay packed and protected when I'm not diving with it. That's too much money for me to want to subject it to the daily wristwatch abuse.
Speaking of straps, though, anybody know the strap width to fit between flanges where the strap pins go? I'm a little surprised the H3 has the kind of wrist band where a single pin failure would let the computer fall off your wrist. I was paranoid about that happening to my Atom. I just replaced the stock wrist band with a Maratac NATO Nitrox-17 band, so I can quit worry about losing it that way.