I see a lot of two overlap in the two SE sites. I think both interest me in the research and possibly the professional work I do. What are some cases to use one and not the other. In particular, when is Data Science the right site for my problem?
The sites should attract somewhat different (but overlapping) user bases. So part of the answer is, what sort of expertise is required to answer the question?
(1) If the best person to answer your question would be a professional statistician, ask on cross-validated.
(2) If the best person to answer your question would be a professional software developer, ask on stackoverflow.
(3) If the best person to answer your question would be a professional data scientist, ask on datascience.
Of course, this is only useful if we're somewhat clear on the distinction between a data scientist and a statistician. This question seems relevant: https://datascience.stackexchange.com/questions/1/what-characterises-the-difference-between-data-science-and-statistics
To elaborate on what I mean by a question you would ask a statistician vs. a data scientist (and bearing in mind that some people could reasonably be called both):
Suited For Cross-Validated but not Data Science
Questions about a general statistical method or concept, either without reference to a particular practical application, or referencing a canned problem:
How do I know whether I should pool variances when performing a two-sampled t-test?
What is the probability of drawing all the hearts from a randomly shuffled deck of cards before drawing any other suit?
Why do normal distributions occur so frequently in nature?
Suited For Cross-Validated and Data Science
Questions about the application of statistical methods to real world problems, especially in problem areas commonly associated with data science (1). Also, questions about specific algorithms used to approach these problems (not just general concepts):
What's a good method for grouping a list of trivia questions by topic?
How best to detect patterns in how the price of a commodity changes over time?
How best to choose the number of clusters for the k-means algorithm?
What are the advantages of logistic regression vs. SVM as an algorithm for classification?
Feature selection for "final" model when performing cross-validation in machine learning
Suited For Data Science
Questions about technologies and frameworks used by data scientists, such as those for managing and processing big data:
Which Big Data technology stack is most suitable for processing tweets, extracting/expanding URLs and pushing (only) new links into 3rd party system?
Horizontally scaling a distributed database, what should I use for a simple key-value store? Cassandra, HBase or Riak? what are the pros and cons?
How important is data locality to Hadoop and Map/Reduce?
(These were example questions offered in the Data Science definition phase)
Suited for Data Science and Stack Overflow
Questions about writing code to solve data science problems, and about the code underlying the technologies used by data scientists:
How to implement a random forest algorithm in python?
How does the MapReduce sort algorithm work?
Suited for Stack Overflow but not Data Science
Pure coding questions. Questions dealing with programming languages (even if they're popular languages among the data science community) that aren't specific to any application of those languages for data science.
How to sort a data frame by columns in R?
How can I prevent SQL injection?
(1) including (but not limited to) clustering, classification, recommendation, data presentation, information retreival, signal processing, machine learning, natural language processing, and anything where scale is a major consideration
I'm sure there will be many questions that could also have been asked on either cross-validated or stackoverflow. But I think there is value in cultivating a community specifically focused on data science, with a knowledge base that sits between those two disciplines. This is more-or-less what I had in mind when I asked "Is your question best answered by a statistician, or a software developer, or a data scientist?"