The faq for both sites is always the best place to check with, in general.
TCS spells out their requirement for discourse that might take place at the graduate level or higher.
Theoretical Computer Science - Stack Exchange is for theoretical computer scientists and researchers in related fields. We welcome research-level questions in theoretical computer science (TCS).
Although there is no black-and-white distinction between research-level questions and non-research-level questions, questions are considered to be "research-level" roughly when they can be discussed between two professors or between two graduate students working on Ph.D.'s, but not usually between a professor and a typical undergraduate student. It does not include questions at the level of difficulty of typical undergraduate course/textbook homework/exercise.
Since Computer Science is still in Beta, it's faq is being worked on continually, but a basic draft can be found here.
From one of the proposals (Alex ten Brink):
Computer Science - Stack Exchange is for students, researchers and practitioners of computer science and related fields. If your question is about ...
- understanding concepts of computer science
- solving computer science problems
- applying computer science to solve problems in other areas
- issues unique to the discipline of computer science itself
In practicality, CS still has quite a bit of algorithm content, but less of a requirement for mathematical rigor (though having such doesn't disqualify a question), and more diversity in terms of applied questions (e.g., Organisation and Architecture of Quantum Computers).