In terms of picture quality, pretty similar. I should also correct myself, as the Breach using a 12 micron sensor doesn't make the resolution better on its own, however it allows for a smaller lens/sensor combo for the same field of view.
With that being said, the Scout III uses a 17 micron, 640x512 Tau2 core, with I believe a 19 mm lens. It has a 18x14 degree field of view (FOV), and a 2x magnification, with 4x digital zoom, and a 30 hz frame rate. It is pretty much exclusively a handheld. Though I believe there are SOME head mounting solutions, this is not what it is meant for. It can detect (note the word detect) a human at 1,246 yards. This means that a human will appear as a pixel at 1,246 yards. To properly ID (PID) you would need to be much, much closer.
The Breach PTQ136 has the new 12 micron, 320x256 Boson core, with a 9.1 mm lens. It has a 24x19 degree FOV, with no optical magnification, and 1-4x digital zoom. With the Boson core, it has a beautiful 60 hz frame rate! This gives it a nice crisp image when moving. There are multiple head mounting solutions, and the after market is starting to pick up with regards to mounting it beside a PVS14. As for detection ranges, I haven't been able to find anything posted, but I would hazard a guess of about 600 yards to detect a human. The Breach also has onboard video and picture recording, which is pretty great! It is also 1 inch shorter, and 5 ounces lighter, than the Scout III. It really is compact!
I guess that's a basic overview. The Scout III 640 will be a great unit, and if you are wanting to have a better chance at ID'ing or detecting at long range, it will be the better option. If you are looking to navigate, or simply use to detect and then use I2 NOD's to ID, then the Breach is the better option, particularly for the price and features. I am really looking forward to having this unit when I got on night walks with my PVS14. I can easily scan the field and determine whether anything is out there. Once I know something is there, I can stalk in with my PVS14 and ID.
It will also be pretty great for rat exterminating on the farm. Spot with Breach, then exterminate with PVS and .22