I've taken both, counseled people on both, but need to say up front I'm not trained specifically in either although I have two psych/counseling degrees. I like DiSC because it's fast and easy and more likely to be clear that it's a "tentative" assessment, something you can modify via behavior and learning at least to some extent. Interpretation emphasizes more the "how do you deal with someone who is different" in a more manageable way. MBTI seems to me to be more difficult for users to understand and relate to, more "magic" and therefore easier for them to believe it is fixed, personality traits they or others are "stuck with."
Rather than give these to clients I usually ask 'what have you taken?" Most have one or the other or one of the many DiSC clones (Colors, Insight, P3 - there are more than a dozen). We go from what they think those mean. The message is people are different, want, need, respond to different approaches - and how can you behave to make the best of that using the skills YOU have, and broadening your repertoire beyond what you tend to do by habit and inclination. That's the major message of such tools in my view, not the specific "this is who and what you are" theory that goes with them.