Moot court also has value because it gets you before the legal community. The judges are often practitioners. This is a great way to meet them and have a chance to demonstrate your ability. It didn't happen to me, but I have seen a judge (attorney) hop off the bench after announcing the results and start recruiting!
Q: Or is the value of moot court a bit over-rated?
I think moot court is greatly under-rated.
Q: Any thoughts or first-hand knowledge would be appreciated.
Think about what your strengths and weaknesses are. Choose activities that will strengthen your areas of weakness. For me, it was application of law to facts. My arguments tend to be fact anemic. Concentrating on law review would probably be close to fatal for me. Moot court requires me to involve facts in my legal arguments. As I think about it, I really can't think of a weakness that moot court wouldn't touch, although if you're weak with the bluebook you'll get a LOT more of that on law review.
BTW, unless you are a 1L or a 2E, it is a bit late to be thinking about moot court or law review. Both programs should be pursued for 2 years starting in the fall for maximum benefit. If you are a 1L, it is a bit early. The important thing in the first year is to get top grades. That will allow you to get on law review and moot court, and have the best options for summer work after the first year. Unlike undergrad work, the first year grades are the most important of your law school career.
3L Chapman University School of Law, Class of '98
[Reprinted with permission https://www.legal.com]