Let’s start his new site with a generalisation, in full knowledge that it’s always dangerous to generalise. That goes double for generalising differences between the Old and New Testaments. But, admitting that I paint with a broad brush, I think there is one that largely holds up.
With that caution, I note that the Hebrew Scriptures are the largely the creation of those in proximity to power. Scribes belonged at courts and temples. The concern they had with law was concern with the running of a country (whether idealistic vision or practical legislation for theocracy). It needed, on the whole, the wealth of kings and large temple complexes in the ancient world, to sustain an industry of producing texts. It is unsurprising therefore that the histories they wrote were the histories of kings.
Prophets seem to have been on hand as advisors to kings, even if their advice was sometimes unwelcome, most of them seem to come and go with full access to some kind of court or entourage. As for the production of poetry and wisdom literature; well, who but the wealthy or well-kept had the time to devote to scribal and literary study?
By contrast, when we move into the New Testament, we move largely away from elite groups. Jesus seems to have crossed most of the social boundaries of his day, but if we can make any deductions at all about a village carpenter whose innermost group were fisherman, we might place him and his core movement as artisan class. Most of those we meet in the urban centres where Paul conducted his mission can probably be placed somewhere between those struggling to survive even at subsistence level and a petite bourgeoisie.
In short, in the Old Testament we meet those who have the power to change their society, and in the New Testament those who have to live in their society with no real expectation of making any kind of difference. Those who suggest a version of religion that is disengaged from the structures of power and politics have forgotten the overt politics of the first, and misunderstood the restraint of the second.