There were definitely some American tanks in Vietnam, but very, very few. In 1974 and 1975, after the Vietnamizing of the war by Nixon, there were North Vietnamese tanks coming south. The North Vietnamese could not use tanks until America withdrew its air support. And America could not use its tanks because the Vietcong had the habit of retreating into places the tanks would get stuck.
That being said, Saigon was taken by North Vietnamese tanks. Saigon was defended by American tanks. The two tank groups never met, being separated by years.
The above shows you have no clue about the Vietnam war. The USMC shipped over a heavy tank battalion of M103, along with a battalion of M50 Ontos, and their LVTP 5 Amtracks.
The US Army had a number of mechanized cavalry regiments in country each with M48A3's and M113's. The M551 Sheridan was sent to two mech cavalry regiments. US airborne forces had the M56 Scorpion with them. The M 42 Duster SPAA was popular as it could put out massive anti-infantry firepower.
All in all, the US had a couple thousand tanks and armored fighting vehicles in Vietnam. The Australians brought in a battalion of Centurian tanks with their forces.
The ARVN had a battalion of M48A3 and several battalions of M41 light tanks (~52 vehicles each). They also had hundreds of M113 APC's. They also had several battalions of old M24 Chaffee light tanks of late WW 2 vintage that were capable of infantry support and taking on NVA light armor, if not the T55 /59.
The 1965 war both sides had western tanks, and it was a draw. The 1971 war India had switched to Soviet tanks, with Pakistan having out dated western tanks, that was a victory for India. I do not believe it can be made a contest between east and west, but if it is, the west lost.
In the Indian-Pakistan wars, Soviet tanks did poorly compared to Western vehicles. In the '65 war, the largest tank battle was Asal Uttar with the Pakistanis losing about a 5 to 1 ratio of Soviet tanks to Indian Western types. That battle accounts for more than 50% of all tank losses in that war.
At Chawinda, both sides were equipped with Western tanks (M48's vs Centurions for the most part) and the losses were virtually even.
At Chumb in 1971, both sides were using Soviet-style tanks, T55's versus Chinese copy T59's. Again, the losses were about even.
American tanks got within sight of the Chinese border. Total victory was at hand. Then the Chinese came over the border. They easily outmaneuvered American tanks, and American lines collapsed. No point in modern American history has retreating American forces been able to turn around and fight. It is our secret weakness. American forces literally outran the Chinese.
In Korea, US and British armor, generally ran the field against N. Korean and Chinese armor. It wasn't US tanks versus Soviet-style armor that allowed China to push UN forces back but simply sheer weight of numbers in infantry. As for the last, you obviously know nothing about the actual fighting in say, the Ardennes Offensive (aka Battle of the Bulge) where US forces did turn around and fight often in ad hoc units and were very effective.
You will say that the Chinese defeated American tanks with other strategies and technologies than tanks, but that does not change the fact their strategies and technologies defeated American tanks.
The Chinese in Korea only succeeded due to sheer numbers. They were willing to take thousands of casualties to take a position held by hundreds of UN troops. UN armored units, US British, or other, operated not only successfully against Chinese and N. Korean armor and almost 100% of the time handed them their asses.
