I don't even know who lost worse.

It was an existential threat to Hanoi, one which they survived. It was largely the byproduct of political football in the USA, plus defense of the sacred cold war "domino theory" beloved of Dean Rusk, Henry Kissenger, et al. The USA would have had to cauterize most of Vietnam and the Mekong River valley in order to prevail, and that would have assumed that China stayed out. Had it gone nuclear we might have had a test case for the nuclear winter hypothesis.

As the threat was greater to the Vietnamese - it was their country - they were prepared to pay a higher price. The problem for the US was that the collateral damage to the economy and society was too high to bear for much longer and yet we were hoist on the petard of our own "Peace with Honor" rhetoric. The wounds and divisions remain in the USA to this day, as they almost certainly do in Vietnam. Those wounds were the price for John Foster Dulles and other Eisenhower Era functionaries having tried to pick up 'the white man's burden' from the French.

 

"It is not necessary to have hope in order to persevere."