From what research I have made to related subjects in passing, the biggest thing is the heavy focus on personal relationships and rampant cronyism/nepotism. In the West, corruption is a very contract-driven and businesslike atmosphere of detached profiteering, where institutions are more like huge machines and money simply filters in regularly to the right people to produce the needed result. Who gets the money doesn't matter so long as things get done and the chain remains unbroken, so if someone Isn't making the right overtures they can be replaced with someone more pliable who can.
This is by no means an all-encompassing definition, since we're talking an entire hemisphere of the planet, but generally things outside the West put a lot more emphasis on Personal Trust, respect for office and dealing with people they know, even if this is not necessarily the Best person for the job. So you see more agreements explicitly built atop friendships and family than you do universal goals everyone is working towards as relative strangers or newcomers with impressive portfolios. People are generally not considered disposable or interchangeable, especially in terms of long-term seniority, because the structure of the whole operation as been cultivated over years of loyalty politics and insular planning, which also makes it extremely hard to break into purely on the basis of being that good at delivering results. Competence is an expected attribute, so its really more of a foot in the door when a friend of a friend to vouch on your behalf is usually the most valuable thing, which means the "everyone knows somebody" factor is extremely high when trying to accomplish anything on a wider scale. Giving gifts is common enough as a social custom its not really seen as a bribe unless it goes far beyond the norm or to the wrong sorts of people, and really-expensive gifts are usually returned in-kind anyway, so that alone is not enough to establish the kind of pull to get the favor you want, even in the places where it is acceptable practice.
A good Heaven-relevant example here would be Venus appointing her once-mortal ex-boyfriend Yaogin to head of the Cerulean Lute, even though he lacked any kind of qualifications for the post, largely as an excuse to keep him out of the way unless he was needed. A less Western bureaucracy would see a lot more of this at all levels, where you have gods privately rearranging their projects as to specifically install close friends or godblooded children they have been grooming for years into senior positions, leveraged on the fact once push comes to shove they Know they will reliably get what they desire out of the situation. Things would be substantially less explicitly mercenary, and more akin to each Division existing as its own "family" in the organized crime sense, interconnected to eachother across webs of interpersonal alliances which have been in place for decades, if not centuries.
