From a purely recreational diving point of view:
The Perdix has a MUCH nicer display. It probably doesn't make a practical difference in clear water on day dives. I mean, if you can read it at a glance, you can read it. But, night dives or dives with crap viz, the difference will make a legit, practical difference. I dived the B29 in Lake Mead a while back. My insta-buddy had a Galileo (not sure if Luna or Sol). Our first dive ended very prematurely because we got down and he couldn't read his tank pressure on his computer and started wigging out that he would run out of air. The viz was only 5 - 10 feet, but it was very dark because of all the silt in the water above us. His backlight was working. He even showed it to me and the DM both to try and get one of us to read it for him. Neither of us understood what he was asking for, so we were no help. But, I did look at his computer and, well, it was not NEARLY as easy to read as a Peridx. I was looking at it with just the backlight on and I also tried shining my light on it.
The Perdix battery is easy to change, easy to find in almost any store, and lasts a pretty long time in the Perdix. And if you happen to screw up and flood the battery compartment, you'll just have to dry it out and put a new battery in to continue using the computer.
If you have a problem with a Perdix, you can email Shearwater and they will respond promptly and take good care of you. But, you are VERY unlikely to have a problem with it.
You can set the Perdix to a lower Conservatism value than the Luna and enjoy longer bottom times (while still staying with the bounds of recreational open water training, by not exceeding your NDL). I really like my Atom computer and I like the Perdix. I would not want to change to a computer that was "more conservative" and gave me shorter NDLs.
The Perdix comes with a screen protector installed and replacements are cheap and easy to put on yourself. And if you ever really scratch the "lens", I believe Shearwater will replace it for you (if you want to bother) for cheap.
The Shearwater comes with nice elastic straps and also bungee and the computer body has holes for the bungee, if you prefer to wear it using bungee instead of the elastic straps. I say "bungee", but I think mine actually came with surgical tubing, but actual bungee cord is super cheap, so I could really use either. Regardless, there are a couple of benefits to all that: One elastic strap or bungee could break, get unclipped, or get cut and the computer still would not fall off. And, there are no strap pins that could break and allow the computer to fall off either. And whether you use the elastic straps or bungee, it will compensate for suit compression to stay snug on your arm.
You said you like AI and the Perdix will work with the transmitter you already have.
A Perdix AI will include a 2 year warranty, which is transferable (in case you find a used one). A used Luna will not come with a warranty, I don't think. If you buy one and it floods, starts acting flakey, or whatever, in 2 or 3 months, you'll just be out the cost of a repair.
A Perdix AI could easily last you the rest of your diving career. A Luna could easily have you wanting to replace it and relatively soon, because either you really want to go back to AI, or you want a more readable display, or both. Or because it flooded after a battery change, or whatever.
(Just teasing!)
