There are people studying this.
Classical Chinese Character Frequency List
Modern Chinese Character Frequency List
Now do your own comparisons because I'm lazy.
Update -- I feel less lazy today so I'll give it a shot.
For obvious purposes, let't take the first 1000 characters in the classical list and see where they go in the trend. I can't do scripts so I'll do excel. Anyway, here are words that are falling out of favor:
- Ancient date and time system: 甲乙丙丁, 子丑寅卯, etc
- Ancient bureaucracy: 丞, 诏, 诛, 朕, 卿, 吏, 郡, etc.
- Some daily words are also fading away: 吾, 汝, 焉, 哉, 勿, 曰, etc.
- Moral concepts: 孝, 贤, 贞, etc.
- Hard to categorize: 骸, 淮, 朔, etc. Either the concepts are no longer popular, or there are substitutes that is becoming popular....