How are they roughly equivalent, let alone "exactly equivalent"? It seems to me that are vast differences any way you compare them.
Economically, there are major differences in who pays them, There are differences in impact/cost. There are also huge moral differences between subsidizing desired behavior, and penalizing undesirable behavior.
Subsidies increase the amount of money in circulation and taxes decrease it. The price of goods is set relative to the amount of money in circulation (this is what inflation does). Hence, exact equivalence of taxing sugar and subsidizing foods without sugar.
No, the effect is amortized over everyone. If you elect to take $100 from half the country or give $100 to the other half it's pretty much exactly equivalent. We saw this experiment with COVID helicopter money causing inflation. You weren't seriously suggesting taxing or subsidizing only one person, were you?
Economically, there are major differences in who pays them, There are differences in impact/cost. There are also huge moral differences between subsidizing desired behavior, and penalizing undesirable behavior.