Um, no. The US was actually extremely soft in Vietnam.

Um, no. The US actually dropped "one million tons of ordnance" on North Vietnam (where US air strikes killed "approximately 52,000 civilians") and "some four million tons of bombs" on South Vietnam ("the most bombed country in the history of aerial warfare—a dubious distinction for an ally"). The US actually supplemented those bombs by dropping about 70 million litres of herbicides on Vietnam, including over 40 million litres of Agent Orange and Agent Orange II, such that "millions of Vietnamese were likely to have been sprayed upon directly" and over 2 million hectares of Vietnam were sprayed repeatedly. (This excludes the anti-personnel gases and tens of thousands of tons of napalm the US employed during the 1960s alone.) And a working group in the US Department of Defense actually reckoned it could substantiate hundreds of reports of US war crimes.

The execution in the "infamous Vietnam execution photo" wasn't even being carried out by a US person; it was not the sort of thing I had in mind. I was thinking more of, e.g., the My Lai massacre.

Is that what you consider "extremely soft"?

The idea that the US had been "tactically winning" the Vietnam war is, so far as I can tell, far from universally held. Can you explain to me why I should believe your description rather than anyone else's?