Both terms are idiotic.
The only term useful for labeling the group of people in question: folks with a certain racial look from China, and from nations around China (Japan, Thailand, Siberia, Korea, etc), is "East Asian". Without that "East" in front the term is useless.
The continent of Asia butts against Europe at the Ural Mountains in Russia, and at the Black Sea, and at the Aegean. It borders Africa at the Gulf of Suez. Everything east of that line to the Pacific is "Asia" . Most of Turkey, and all of Israel, Lebanon, and the entire Middle East east of Egypt, are part of "Asia", and so is most of the old soviet union, Iran, and the entire Indian subcontinent.
In the U.K. the word "Asian" usually refers to folks from the Indian Subcontinent (who should be called "South Asians" . In the US its now used as the substitute for the word "Oriental" to mean "east Asians". So you get confusion between Brits and Americans on top of the other problems.
A book I read informed me that "must Muslims are Asian and not Arab" (its true that the biggest Muslim population countries are non Arab countries of southeast Asia, but the Arabian Peninsula is part of Asia, so Arabs ARE also Asians!).
"Oriental" isn't particulary offensive. But it is old fashioned and ambiguous ( my parents generation used "oriental" to mean "Arab" or "west Asian" (like "Oriental Carpets", and "Oriental Jews"), us boomers, and younger folks in the US use "oriental" to mean "East Asian"). The term just lept from west Asia to China/Japan/Vietnam overnight, and skipped the middle part of asia, and no one knows why.