--Galileo supports audible alarms, Petrel does not.
--Galileo supports more gasses than Petrel. Probably not a big deal, since petrel supports more gasses than I will be using for quite some time.
--Log downloads are easier on Galileo than they are on petrel. It's only a very minor annoyance. Since petrel uses Bluetooth and the radio consumes battery, you have to initiate communication via petrel menus each time you want to use it. Galileo uses IRDA, and the IRDA is always active when the computer is on. Before I bought the petrel, I thought the Bluetooth would be better than the IRDA. I was wrong.
--Galileo is fully configurable over the data connection.
--Most configurable things can be changed during a dive on petrel. Galileo will not let you change settings during a dive - you have to surface to modify things. I've only been on one dive where I actually wanted to do this, but it has happened.
--The petrel can accept standard batteries. This is a biggie. Galileo takes only special batteries that you've got to pay a scubapro a premium price for. Petrel can accept expensive long life batteries, but it can also take regular AA rechargeable or disposables. The expensive long life petrel battery is less than half of what the Galileo battery costs.
--Petrel is cheaper than Galileo. Even the Luna costs more than Petrel. Sol costs more than Luna.
So... yea I put a lot of weight into the readability of the display. If you haven't seen a petrel in person, you should have a look before you make the decision.
Petrel thankfully doesn't have audible alarms but it does do something nifty with color changing background to help you see what it wants you to see.
To me, bluetooth that takes 3 button pushes to activate is way easier than finding a little IR dongle and plugging it in.
It is really nice to be able to change settings and gas mixes underwater, even if you should catch all that during predive checks...
Battery deal is HUGE. AA you can get almost anywhere. I've never heard of the battery used in the Sol...
Shearwater has some of the best customer service in the industry. Scubapro has a history of changing customer service repair and return rules, and they might want you to go through a dealer.
I see three tiny buttons on top of the Sol, 50% more to remember the function of than the Petrel. Does the Sol display the button function on the screen during use? It's nice to not have to remember exactly what the button does because it's always labeled, and there's only two of them...
Sol has air integration, a compass, and a heart rate monitor, and it's probably a nice computer.
The Petrel is better in some ways, lacks some bells and whistles that aren't necessary, is made by a company with industry leading customer service, and is cheaper!
Try to see them both in person. Don't read the manual. Try to set up a gas and change some settings, and do it all in the sunlight.