Difference between "content" and "contentment"?

Given this sentence:

I find (content/contentment) when sitting on a crowded subway train.

or in the sentence fragment:

my place of (content/contentment)

In the dictionary, I see that content (as a noun) means "a state of satisfaction" and contentment means "a state of happiness and satisfaction". Therefore I am unsure of which one to use. Does the difference come down to formality or is there a proper use case for each one?

Use contentment. The sense of content as a synonym for contentment is no longer in use, except as a component of set phrases like [my] heart's content.

The American Heritage Dictionary defines content (n.) as

1. something contained, as in a receptacle.
2. individual items in a publication or document; material that constitutes a document.
3. a. substance or significance of a work, especially as contrasted with its form.
4. The proportion of a specified substance: Eggs have a high protein content.

and finally (with a different pronunciation)

Contentment; satisfaction.

The noun content is not often used to indicate the state of being happy.

It is, however, used as an adjective or transitive verb with that meaning, e.g. I am content/he contented himself with one piece of cake.