Here's something from MW Vocabulary Builder:

"inherent...

Part of something by nature or habit....

Inherent literally refers to something that 'sticks in' or is 'stuck in' something else. A plan may have an inherent flaw that will cause it to fail; a person may have inherent virtues that will bring him or her love and respect. Something inherent cannot be removed" (170).

MW Collegiate:

"intrinsic: belonging to the essential nature or constitution of a thing (the ~ worth of a gem); b: being or relating to a semiconductor in which the concentration of charge carriers is characteristic of the material itself instead of the content of any impurities it contains 2: originating or situated within the body or part acted on"

It seems that 'inherent' tends to bend toward values and 'intrinsic' can subsume both values and physical properties.

I haven't checked onelook.com, but if you check there, you'll have dozens of references that may give you more clarification. There are sentences in which I think the two terms can be interchangeable, as you mentioned, but others in which one would be more preferable than the other. If the sentence strongly indicated a clear moral value, I'd use inherent over intrinsic...but maybe not. It really would depend upon the specific sentence, so I'd probably consult several references if uncertain about the choice.