Pros
You have access to almost any high-level executive. Korn/Ferry has great brand recognition, so people are very likely to take your call or return your call/email. Associate-level positions would be great for recent university grads who want to do this for a living or who want to do it for a few years before grad school. If you're not a recent graduate, take very careful consideration before accepting an associate role. Principal and Senior Client Partner level positions would be great for people coming from years at a different search firm or a late career switch from an industry in which you can be an expert with a great network.
Cons
If you are working at the associate level, be sure that executive search is really something that you want to do (possibly for the rest of your life). You will build a great network, but you won't develop many (if any at all) transferable skills. Be prepared to perform tasks that, although perfectly legal, might leave an icky taste in your mouth. Depending who your immediate supervisor is, your life at Korn/Ferry can either be heaven or hell. People who have climbed the ranks of recruiting haven't gotten there by being good leaders of others, so it really depends on compatibility with the personality of your supervisor. Like any role with any company, your supervisor holds the cards as to whether or not you will ever be promoted, but Korn/Ferry lacks a formal HR department if there are ever any problems.