I personally think that the most appropriate answer is: it depends. Specifically what is "Markowitz's mean-variance model"?
If we consider the more general definition it is an optimization framework and the portfolio is obtained by optimizing according to an objective function and it is expression of the estimated mean/return component and variance/risk component.
First of all the point is how one estimates the inputs (which assumptions, models, statistical techniques etc.) and secondly how one defines performance.
If we only consider the vanilla (no constraints etc.) minimum variance portfolio and vanilla growth optimal portfolio and supposedly we compute the variance component equally all becomes a question of how one estimates the mean component required to obtain the second portfolio.
Finally if we suppose that the estimated mean component is quite close to one's expectation and performance is intended "stability" or "Sharpe-ratio" it happens that the growth optimal portfolio is less diversified and riskier/more volatile (at the same time it compound the invested capital faster thus delivering a higher terminal wealth).
Both Samuelson (1971) and Markowitz (1976) implied that many investors are willing to sacrifice long-term return in exchange for short-term stability.