Perhaps you need to read one of the many explanations of those terms, which make it clear that they are not mutually exclusive. For example "‘America Is a Republic, Not a Democracy’ Is a Dangerous—And Wrong—Argument" by The Atlantic.[0]
To steelman your position a little, let me assume that you meant "direct democracy" and "indirect democracy" respectively. However, I don't think anyone is proposing a completely direct democracy, where every decision is put to a referendum.
Also, even if there is some merit in dampening the underlying volatility and limiting the power of small majorities, it's not clear that gerrymandering (or the electoral college, or whatever else you had in mind) actually works to prevent extreme outcomes.
If anything, the current lack of democracy in the US conditions a minority of voters (not to mention a minority of citizens) to expect over-representation in the corridors of power, and, as we saw on 1/6, it is pandering to the will of the minority that is most likely to lead to the rule of the mob, nationally.
[0] https://www.theatlantic.com/ideas/archive/2020/11/yes-consti...