I handle it that a DC 10 gives you the traits of the type of creature.

For example, religion 10 allows you to recognize an undead and know about the non-living, crit immune, negative/positve energy kinda stuff. If you fail that you might know some truths, but otherwise be under some kind of common misconception.

Making the DC 10 + CR check lets you know the name of the creature and what is written in the basic fluff text, but no specifics.

From then on I handle the information in intervals of 5, going by how distinctive a specific feature is. If a creature has spellcasting or is straight up immune to something by means other than (sub)typing, that is included in beating the DC by 5. It basically gives you a general idea of the enemy's main capabilties.

Beating it by 10 gives you more specifics on its main abilities, like the level of its spellcasting or how its attacks work exactly. Some parts may be left out, but you now have a pretty good idea of how to go about fighting this kind of creature.

Beating it by 15 is enough to give you a general run down of all its capabilities. For a standard member of this particular creature type, you know each thing it can do in pretty good detail.

Beating the DC by a full 20 essentially lets you look at its stats screen. You know if this individual creature exhibits special traits normal members don't, you know what its good/bad saves and ability scores are, and so forth.

In the case of templates, I run a separate check with all DCs increased by 5.

In the case of creatures that have significant advancement tables, like Dragons, I base the DC on the weakest version, but you don't learn about the abilities they gain during advancement unless you beat that DC as well; so for example you might know everything there is to know about a Wyrmling, and have an idea of how an adult differs from it, but have no idea how a great wyrm differs from an adult.