Aren't MBTI and Big 5 connected? I have seen repeated suggestions that the Big 5 model is the preferred model of personality in psychology, and Myers-Briggs is used in pop psychology and industry and not presently taken that seriously by proper psychologists.

It seems to me that there is a connection between the two. Extraversion is one axis with the same name and similar or unchanged content. Openness on at least one test sounds like a rough gauge of old-fashioned IQ, and as such is a candidate for correlation with the Sensate-Intuitive axis. In the popular Please Understand Me!, the SP-SJ distinction sounds a lot like Conscientiousness. These suggestions could be challenged, but it seems grounds to suggest that three of the four Jungian preferences survive largely intact in Big 5.

Am I overestimating the continuity between the two models? If I am not, why does Big 5 have scientific validity where the MBTI is a bit of fluffy pop psychology?

--UPDATE--

I have un-accepted the answer as I find it bare assertion plus a statement of author's credentials, and I really want a more thorough response.

To flesh out what I meant by the question, I'm going to go with Jungian preferences as simplified in Please Understand Me!, said to be one more assertion of temperament theory as Kevin Trudeau's Mega Memory can be said to be one more assertion of (neo?)-classical standard memory techniques, which may be seen as a move from fluff to fluffier. I acknowledge this as a liability, and I further acknowledge that I do not engage whether the NT-NF polarity is relevant to people deemed Sensate, nor whether the SJ-SP polarity is relevant to people deemed Intuitive.

One can be deemed Intuitive without being good at, relying, or identifying with intuition as the term is usually used. The Sensate-Intuitive axis is one I would on consideration suggest might be better named Concrete-Abstract: where Abstract is paired with Feeling, it matches more closely with what one might pick a one-word label of "intuitive" for (other candidates might be "influencer, "spiritual" or "self-actualizing"). Combine Abstract with Thinking and you get STEM practitioners, analytic philosophers, and so on, and possibly liable not to hold common intuition in very high regard.

I don't think I have anything quite as striking to offer for the SP-SJ axis, but I think that people evaluated by Myers-Briggs as SJ with at least a square J, you'll get people who are diligent, believe in order, and so on, high performers on high Conscientiousness. I'm a little less sure with SP, but I would think squarely SP people would commonly register as highly primative, and I would expect solid SP's to score low on questions about "I diligently keep my home, my room, my cubicle, and my desk meticulously clean" used to assess degree of Conscientiousness on Big 5 scoring.

I assume that Extraversion will be accepted as an obvious point of contact, and people may argue traits versus preferences (Quiet: The Power of Introverts in a World that Can't Stop Talking asserts that one can be deeply introverted and learn to function as a consummate extravert if one deeply desires it), but it still looks to me like, if I may count better, all three other Jungian preferences appear to reincarnate in Big 5 in slightly different form.

If industry's popular MBTI is largely reincarnate in proper psychology's Big 5, it might explain why industry is reaping apparent benefits from the deprecated tool.

If Openness, which is said to be a crystallization of what is otherwise represented in IQ, is largely similar to "Sensate-Intuitive" (or "Abstract-Concrete"), and so on, and a personality psychologist does not see a need to give much more than bare assertion in a response, could this be a little more worth digging into...
All personality models are related in that they are carving up the same variance into different factors, and some of the factors will overlap. Extraversion is probably the most similar trait between the two models, but it's still quite different.

As a personality psychologist, I would say yes, this is potentially an overestimation of their convergence. A brief description of why the Big Five is preferred over MBTI is that the measures of the former are dimensional rather than categorical, have more test re-test stability, and have more stable relationships with other levels of analysis (e.g., genes predicting traits; traits predicting behaviors). Reliability and validity are the cornerstones of quality measurement.