Patagonia Coldbore has been around longer and is a more robust solution without the need for addons.
Both are very good, but the basic CB1 license gives you the full desktop solution which is equal to the AB $200 Desktop, plus you get a linked license for a Trimble (Windows Mobile) and then a Windows Phone License. I use a Windows Phone with no sim card.
What holds CB1 back is Gus is tied to Windows and his license set up is clunky. Plus being from Argentina he mostly stays to himself outside of that country. Though Gus is very active in ballistics and is branching out more so. But Bryan is a much better marketer and ambassador for his product than Gus is.
Patagonia's Engine is better, it's much more robust with modern fixes. AB is 3DOF, CB is a more of 4DOF solution, Modified Point Mass engine what actually knows what is going with the bullet during flight. In most software there is no bullet, it's just in a point in space and time, but CB1 knows where the bullet was, and where it is going. AB is based on McCoy which is pretty common, but CB uses Pesja which addresses many of the shortcomings of McCoy. If you read the Pesja books they contradict a lot more than people realize.
The CB Desktop is great, very robust, lots of charts and graphics, it's the best tool for making offline data. Plus you can link to an OneDrive and move the tracks around. I can build a track on the phone, and then when I connect to the internet, upload to the cloud and then pull it into the desktop. it also connects via a Trimble to a lot of devices.
Lots of guys on here have been using it for a long time because it's been around longer than most.
If you are not using a Trimble, or Windows Phone, in the field CB falls down to AB. Their software is better suited to the field, mainly because of the Kestrel, but their App is available on better platforms. Windows sucks, Gus is too tied to it because he worked for Microsoft back in the day. If CB was tied to more devices you'd hear more about it, it's super robust and does a better job without the truing.
However, to crunch numbers, build charts, and to use back at the house, it's better.
You tend to get what you put into it, AB is easy because it's everywhere and within the limits of most shooting, works very well. But you have to put a lot of effort into it. CB can do the same thing with less effort, however people hate carrying the big Trimble units around, which makes sense. A Kestrel is awesome in the field, small light, effective.
It's worth the run, especially at the price point, you get a lot.