Expanding on my earlier comment:
If an interviewer decides to ask you about being a mod, how are you going to frame your response?
I think the number one rule for a resume is be able to talk about anything you list. Usually, people mention this rule in the context of resume, ah, "embellishments," which is not an issue for you. You do, however, need to think about exactly what you're going to say, once you're asked to say more.
Just as there are a lot of different ways to moderate effectively, there are a lot of different ways to describe being a mod. You mentioned that you've talked to interviewers about moderating before. Thinking back, what did you say? Did you sound like you were talking about a job, a hobby, or something else? Were you focusing on mechanical details? Stories/experiences you've had while dealing with people as a mod? Other points? How much time do you spend moderating, and how much do you prioritize it over other things in your life? These questions don't have "right" answers, but they should be helpful if you know how you want to present yourself.
This ties into a great point that Air made earlier: the type of resume you're writing makes a difference here. I wouldn't consider "moderator of Code Review SE" — or, for that matter, even "moderator of Stack Overflow" — to be relevant experience for a computer software position. If you were applying for "community organizer" or "project manager," it might be a different story.
That said, when I was looking for my first few internships/jobs, I put non-relevant experience on my resume because I figured some employment was better than nothing at all. (Hmm... I wonder how many Americans haven't worked at McDonald's at some point in their lives....)
I think the best way to use your mod experience here (regardless of how you list it) would be as an opening for yourself in the interview. Segue from the description of being a moderator into a description of Code Review itself and then the software skills you clearly have to be a 25k user there (and what you've learned from participating there). Heck, your second-most-upvoted answer is to a question titled "Implementing a proper linked list for a professional environment"!
Finally, one potential pitfall with choosing the "work experience" route: be aware that you could be unwittingly sending signals that you don't want. Some potential employers may figure that being a mod is a paid position because you list it as work experience. This could even get you into trouble later on if you get the job, choose to continue moderating, and your boss notices. Don't assume you'll be able to explain it away in the interview or before any damage is done; someone may make a silent assumption without ever explicitly asking you about it.