Actually, if Twitter were to play fair, I think they would restrict Chinese users to 46 characters, since there are 3 bytes / UTF-8 encoded Chinese character, and only 1 byte / English letter.  Alternately, in terms of number of bytes, the right comparison is probably between 140 characters of Chinese and 420 characters of English.

Consider the differences in the three:

"Please stand back from the doors"  (English) (1)

請勿靠近車門                             (Modern Chinese) (2)

勿近車門                                  (Classical Chinese) (3)

If you take a "symbol" to refer to a byte of data (and assume UTF-8 encoding for (2) and (3)), then the E(1) = 3.8 , E(2) = 2.6 , and E(3) = 2.0: so "information content" of a series of bytes-as-symbols actually drops as you move from English to Classical Chinese.  

However, as you note, a character in Chinese maps to a meaning. So let's map each of the meanings to a series of symbols and calculate the entropies.  Also rewrite (1) as "Please don't get close to the doors" to make it easier to compare the mappings across languages:

"Please don't move near the car doors." -> "A B C D E F G"   (1) = 2.5

"請勿靠近車門" -> "ABCDFG" (2) = 2.6

"勿近車門"      -> "BDFG" (3) = 2.0

So in this case the information content of (2) increases over (1), due to the repeated inclusion of spaces in (1). (3) remains constant.  These trends would accelerate with longer texts and almost certainly the classical Chinese version would quickly become the most "entropic." 

Why would it do so?  Because both (1) and (2) incorporate more redundancy than Classical Chinese.  Another interesting thing to consider is the problem of error correction, which becomes a concern when concerning codings.  You might want to think about how much repetition is present in English versus modern Chinese versus classical Chinese, and why that is: I would argue that Classical Chinese is minimally repetitive and maximally entropic, in the sense that Classical Chinese uses the bare minimum of symbols necessary to convey a thought. Contrast with English or even Modern Chinese, both of which have repetitive characters (spaces in English and words like "the"/"an", symbols like 的/个 in Modern Chinese , the far greater frequency of compound-character words in MC ex 绵羊／山羊 instead of 羊) that help preserve the meaning of a message in transmission. In human languages, preservation of the message entails the addition of extra words (just think how verbose English law is - there's a reason for that); in formal codings, preservation of the message entails the addition of extra bits.  

Anyways, these are just some random thoughts that might help you think of ways to begin quantifying the differences in "consumption of symbols" you note in Twitter feed.