More of one's working knowledge is loaded into the specifics of vocabulary in classical Chinese, whereas more of one's working knowledge is loaded into grammar in classical Sanskrit. At least it seems so at first. Wrestling with the complexities of compounds in Sanskrit and syntax in Chinese blurs this distinction though. The animating morphologies transcend the vocabulary/grammar distinction in highly modular languages.

At bottom both Chinese and Sanskrit, like many other classical languages (Latin, Greek, Arabic), are quite modular. While Chinese's phanopoetic menagerie may not at first glance appear as RISC-y as Sanskrit's lexis (comparing radicals to roots may not be fair anyway), basically it's rare in both languages to stumble across a word that is just a black box, whose etymology you can't pull apart so as to guess what it means. Rarer, at least, than modern languages, which seem more atomized and dictionary dependent, as opposed to the classical languages, which by their systematic modularity were able to function as universalist languages of empire.