I don't know what you mean by that. "Compound" usually refers to a word spelled with multiple kanji. There are many words in Japanese like that.
In Chinese however, basically all words are hanzi compounds, or so I've been told. I don't actually speak either Chinese language though. I would imagine there are some handful to hundreds of single-syllable single-character words.
I, too, am a bit confused by what you mean by ‘compounds’. Do you mean words that are made up of two characters? In Chinese there are plenty of words that are one-character as well as plenty that are two-character. Look at this example.
我不会说中文。I can’t speak Chinese.
Note the number of characters for each English word.
我 = I (one-character)
不会 = cannot (two-character)
说 = speak (one-character)
中文 = Chinese language (two-character)
Or do you mean the ‘pieces’ (the ‘radicals’) that make up individual characters? Look at these three characters:
Look at the left side of each character. All three characters contain the radical for ‘human being’ on the left side.
Chinese makes use of single-character and compound words extensively; I used to call Chinese "advanced kanji practice" because the entire written system is hanzi. Perhaps it looks like Japanese has more because they're more obvious in contrast to hiragana and katakana, but Chinese has more characters in common use by far.
There is a lot of information on the Internet about compound words (熟語) in Chinese and Japanese, but unfortunately I cannot find any information about the number of compound words in either language. So it is hard to say. The best I can do is refer you to these two pages:
h ttps://en.wiktionary.org/wiki/Category:Japanese_compound_words [Remove the space after the first h.]
h ttps://en.wiktionary.org/wiki/Category:Chinese_compound_words [Remove the space after the first h.]
You may wish to take a look at both of these webpages and get an idea as to how many compound words are listed on each webpage.