On the chance you may mean tanks when you say "armor", I'll give you a different angle on the question than the above post.
In the 1960s, both the US and the Soviet Union were preparing for World War III with Europe as the main battlefield, so the tanks employed in Vietnam were ones designed to win a European war. This meant they didn't make much sense in Vietnam, but both sides used them.
The main American battle tank during that time was the M-60, a reliable and simply designed tank with decent firepower and maneuverability. They were mass produced in the thousands and mostly used to secure bases and highways during the Vietnam conflict.
Our main battle tank today is the M1A1 Abrams, which is vastly superior to the M-60. It has a low profile, reactive armor, is much faster, has a bigger cannon and computerized fire control. But it also is more expensive and breaks down more easily.
The main battle tank for the Soviet Union and North Vietnam at the time was the T-55. It was functional, but had some serious shortcomings. The Soviets are known for successful tank design, and the T-55 was followed by vastly improved T-72s and T-80s, both used into the 1990s and found in armies around the world today.
My dad was deployed to Vietnam during the war, and my husband has been deployed to Iraq twice in the past couple of years; so I'll list the differences from a soldier's perspective.
During Vietnam, American troops wore flak jackets or vests. The term "flak" comes from the German word "Fliegerabwehrkanone" which literally means "antiaircraft gun." You can see why GIs shortened it to "flak"! The jackets had plates sewn into pocket-type areas to stop bullets, shrapnel, etc. They were heavy and bulky, but they are not actually as heavy as the current armor that soldiers wear. The helmets during Vietnam were basically the same shape, but they were made out of steel.
Today's soldiers still wear versions of the flak vests, but they have easy-to-remove Kevlar plates. With the plates in and with full armor on, a soldier can weigh upwards of 60 pounds more than his normal weight. Part of this is because the armor has different parts to attach to the vest and even some leg armor. The helmets look similar, but instead of being one colored, they are camouflage and made out of Kevlar. Soldiers can put padding (much like the kind that goes in a football player's helmet) inside the helmet to make it fit better and to make it more comfortable. The theory in switching from steel to Kevlar is that it supposedly stops shrapnel better, and since IEDs have become the weapon of choice for many insurgents and enemy combatant, that is highly important.
One last note, soldiers in Vietnam had a lot more lenency about whether they wore their armor. Part of this is because it was so hot and humid in Vietnam. Modern-day soldiers do not have such a choice and, with the advance of weaponology, would probably choose to wear the armor anyway anytime that they are outside the wire.