"Something as Received" versus "Receiving Something"
Solution 1:
I think you have already identified the difference in your question.
In phrase 1 the verb "learning" is referenced in both "receiving wisdom" and "learning the hard way".
In phrase 2 "received wisdom" is a noun phrase, whereas "learning the hard way" is a verb phrase. To create symmetry, you could write "Received wisdom is better than that learned the hard way." Where "that" refers to wisdom or a learned concept.
Solution 2:
Here's what I think.
Receiving and received are both participles, respectively the present and past.
Sentence 1)
Present participles are used as gerunds so we can talk about actions as things, and gerunds are used as nouns, generally with a pretty broad scope. The gerund swimming really includes the whole idea of swimming, not simply the action of it. They're also used as adjectives but in a peculiar way.
So what is the participle receiving doing in your subject? Is it a gerund or an adjective? As an adjective it would be describing wisdom as a thing that receives, but that doesn't make sense - so we can eliminate that interpretation. As a gerund its the whole idea of receiving compounded with wisdom, which is hard to interpret meaningfully, so we can eliminate that too, and we're pretty much left with nonsense (even though I know what you mean). In any case, the participle cannot function as a continuous verb without an auxiliary form of be.
But there is a way to rescue this.
To infinitives can also be used as nouns, and they compound much more readily with other nouns. Infinitives have a narrow scope compared to gerunds; they represent the action itself or the doing of the action. So you could say, and it would be meaningful and correct to do so, To receive wisdom is better than learning the hard way, but there's still a problem. The idiom, learning the hard way is not specific to wisdom, it just means learning by trial and error, and we can learn practically anything that way. So I think the sentence would need to be restructured as follows:
To receive wisdom is better than learning it the hard way.
You really need that pronoun for the sentence to be meaningful.
Sentence 2)
The noun group received wisdom uses the past participle as an adjective to describe a kind of wisdom. That's fine, and the phrase has been in use long enough to have an accepted meaning related to the similar phrase received ideas. These refer to conventional notions that are received through culture; they are received passively and generally accepted as true without much, if any critical thought or even awareness.
Now let's take a look at the object of your sentence - learning the hard way. It uses the gerund learning compounded with the noun phrase the hard way, and it also has the widely accepted meaning noted above. The problem is that these things don't compare well because they are so different. Received wisdom is one thing, and learning the hard way is another.
But hey, I do know what you mean, even if these sentences aren't quite sensible. Here's how you could say it.
Received wisdom is better than wisdom learned the hard way.
I wouldn't agree with this statement as received wisdom is not generally considered wise, where learned wisdom generally is, or at least has a better shot at being authentic.
But perhaps the meaning you're really after is that it is better if you can receive wisdom by observing others, reading or from a good teacher, than to acquire it through the school of hard knocks.
Perhaps you could say something like:
Receiving wisdom from books and teachers is better than learning the hard way.
Regarding mood, I think your sentence is in the indicative, which is used to ask questions and to state facts and opinions. Clearly, your statement expresses an opinion.
Solution 3:
You ask:
What type of grammatical principle explains "wisdom as received" or "received wisdom" (as in 2) an a part of speech other than a verb phrase? Is this an example of grammatical mood? If so, what mood is this?
However, I think it (especially #2) relates to idioms rather than moods.
Grammatical mood applies to verbs, not nouns. Received wisdom is a noun phrase, so no grammatical mood applies.
received wisdom (redirects to conventional wisdom as a synonym) A belief or set of beliefs that is widely accepted, especially one which may be questionable on close examination. - wiktionary
conventional wisdom Conventional wisdom is the body of ideas or explanations generally accepted as true by the public and/or by experts in a field. - wikipedia
learning the hard way Learning the hard way refers to the educational results developed in the process of living life, the perspective gained as a result of trial and error—more often used in reference to the mistakes, mis-steps and misunderstandings which lead to better judgment. - wikipedia
The contrast is between received wisdom and learning the hard way, that is, to accept what others accept or to suffer your own mistakes.
The phrase "receiving wisdom" isn't idiomatic as a synonym for received wisdom or conventional wisdom. Sentence #1 attempts to contrast the gaining of wisdom with suffering one's own mistakes. It's not completely satisfying as a contrast because 'the hard way' can yield wisdom of its own.
Sentence #2 contrasts the two idiomatic formulae.