There are a number of problems with the assumptions behind this question.

"Was" at what period of history? What evidence is there of this difference in literacy rates? And if there is such evidence, is there any evidence that the writing system was the cause of difference in literacy rates?

Lots of factors besides a language's writing system -- social, economic, political -- can affect literacy rates.

At present, China's literacy rate is somewhat higher than the world average, as is Taiwan's, although Chinese is still written with characters rather than with an alphabet.

And as to China being "stuck" with its writing system, there are various good arguments for maintaining that system, because of the small number of possible syllables in the language, as well as the vast differences in pronunciation among dialects.

Looking across world scripts, there is no real correlation between the 'difficulty' of a script and levels of literacy. More often than not, if literacy is low, it's because the importers of the technology of literacy wanted to keep it that way, or because literacy had low utility in daily life.

One of the better books on the various inventions of writing is The First Writing by Stephen Houston.

Also good for understanding value judgments in script (whether a script is good or bad, or whether one is better than the other): Unger, J. Marshall, and John DeFrancis. 1995. “Logographic and semasiographic writing systems: A critique of Sampson's classification,” in Insup Taylor, & David R. Olson, eds. Scripts and literacy: Reading and learning to read alphabets, syllabaries and characters. (Neuropsychology and cognition 7), pp. 45-58.