If you mean European and American powers as "Occident" as opposed to Asian powers as the "Orient," which seems most likely, the West is the safer bet than the East. Let’s take a map to start with.
Some countries that largely draw their cultural, linguistic, and legal heritage from Europe. These are the "Occident," if you will. Some countries referred to as part of the "global south," because they’re not in NATO. Some of them have more significant non-European heritage than others.
Some countries that are characterized by being entirely or almost entirely Muslim states. Historically speaking, these (along with Russia) were often referred to as the “Orient,” but they have very little in common with, say, China.
Some Asian countries that are not predominantly Muslim. The Indian subcontinent is notably different than the eastern Asian countries. Mongolia is something of a special case as well as not being significant on the world stage anymore. You might mean something like this when you say "the Orient."
Some countries that don’t fit neatly into the above categories. They’re post-colonial countries with significant Western influences overlaid on top of an existing culture that wasn’t lost along the way.
Nobody really knows for sure.
Trying to predict the future is a tricky business. Europe and the United States could politically self-destruct; they might not. However, the safe bet is that things will look similar to how they looked before. On the scale of great powers, history moves relatively slowly. Major powers often last a long time.
130 years ago, in 1890, the United States had the second or third largest economic engine in the world, depending on how you measure it. In 2020, the United States had the second or third largest economic engine in the world, depending on how you measure it.
In 1890, Britain was clearly the strongest global military power with the farthest-spread empire. 130 years previously, in 1760, Britain was clearly the strongest global military power with the farthest-spread empire.
The Romans spent several centuries as the major power of Europe, North Africa, and the Middle East.
There is one wild card that doesn’t depend much on politics: Global warming.
Notice something about the red and green countries? They’re mostly concentrated at tropical latitudes. Global warming puts countries like India and Indonesia on the horns of a dilemma: Addressing global warming means cutting global carbon emissions. On the other hand, aggressive economic growth (such as seen in China) means significant increases in carbon emissions.
Tropical countries are the ones most harmed by global warming, and that includes a lot of the “Orient,” whichever way you choose to define it. The decisive world-wide action that would put a halt to global warming in the near-term and prevent large-scale difficulties for tropical countries by 2150 would also likely cripple the high-growth engines in developing countries.