When an investor values a company, why is DDM inappropriate to value a company in which the investor is considering to acquire a controlling stake?

Because the investor would have control of ALL cash flow, not just the cash flow available after debt obligations, capex, etc.

Theoretically the difference in Valuation between DDM and FCF is the discount /premium one would pay for control. A more interesting question is: these models will almost always yeild different answers so is the difference truly due to the “premium” or is it because the models aren’t really very accurate? Can we break the delta in price into two parts: noise + actual premium? If so, how much is the “noise”? That is, is a 5% difference not significant; what about 10% etc?