Asrock was a side branch that had slightly been part of asus, and now has more or less became its own brand. as for your question:
Quality: Asus has highest quality, But Asrock puts more features on their boards for less than asus does(as asus boards have a premium cost)
Compatibility: compatibility is all depending on the motherboard model itself rather than the brand. compatibility issues are usually fixed with bios updates if necessary.
Reliability: both can make fine sub 200$ motherboards. the extreme4 series(including m albeit its micro so theres less room inbetween pci-e slots) has the best potential for its price range, Asus is just more reliable hardware as they have alot of experience with hardware and is a large name brand.