It sounds as though you are trying to write about the difference between wealth and nobility.
One who is poor financially is in poverty, or economically destitute, or bankrupt, though the last one is also a technical term. One who is poor in ethical qualities could be called inethical, immoral, abhorrent, crude, or any other number of words to describe one who is poorly-behaved. VERY specifically, if it is someone who doesn't share their money, you could say they are "cheap" or "a miser" or, more kindly, a "spendthrift" if they always spend as little as possible on their ventures.
Metaphorically, one who has no moral guidance or standards can also be called 'Bankrupt', though usually it is specifically called 'morally bankrupt' - meaning this would be two words, not one.
Financial richness has quite a few terms to describe it: wealthy, well-off, well-to-do, or one could be a millionaire, billionaire, or even trillionaire (All three being categorical). Whereas being rich in an ethical sense would be honorable, noble, decent, kind-hearted, and willing to share wealth would be generous, philanthropic/philanthropist, and charitable.
I believe the term you're looking to use depends on the exact nature you are trying to express in the person you're describing. Are they very willing to offer their wealth, even if they have little? Are they individuals who are incredibly wealthy, but who refuse to hand out their wealth? Or is it the grace of the person that you are judging? As in a poor individual who acts with dignity, or a wealthy individual who acts very cruel?
There is certainly a multitude of metaphors connecting wealth with virtue. Even "noble" has the connotation of being one of a higher-class and, therefore, wealthier than others (though this is a connotation, and in actuality nobles are not always wealthy). Rich in virtue, poor in manners, there's quite a lot of ways you can phrase what you want to say.
Best Answer
Theoxeny I recall this term from Greek mythology, but I don't know of it equates to love of strangers compared to family
[1]: http://Xenia (Greek: ξενία, xenía, trans. ... Theoxeny or theoxenia is a theme in Greek mythology in which human beings demonstrate their virtue or piety by extending hospitality to a humble stranger (xenos), who turns out to be a disguised deity (theos) with the capacity to bestow rewards.
Xenia (Greek) - Wikipedia
What the OP describes is an extremely common psychological phenomenon. I'm interested if there's a more specific answer.