There are no similarities at all except that the anti war brigade use the same slogans.
Vietnam was all about a country which was divided into two after the French pulled out following their defeat at Dien Bien Phu, with one half (the North) being communist and the other capitalist.
The communists supported by China and Russia invaded the capitalist south which had a treaty with the U.S.
A poular theory at the time was the domino theory which was that communism would spread through south east asia by one country falling after another, and in those days many people were afraid of communism.
Therefore the U.S and Australia gave aid to South Vietnam, whilst the British fought the communists in Malaya (and won).
Iraq is totally different. Iraq was invented as a country in the 1930's out of a number of tribal areas governed by the British, including Kurds, Marsh Arabs, Bedouin, and Mespotanians so historically it is a made up country anyway.
The invasion of Iraq was for a number of reasons but in effect to depose the secular Baathist regime there and establish a new government. The military forces were defeated in conventional battle and now there is a security vacuum which is drawing in terrorists and insurgents from across the Arab world.
These insurgents are killing civilians, Shi'ite Muslims, Kurds and occasionally coalition soldiers.
The war in Iraq lasted three weeks and since then it has been about supressing insurgency whilst the new Iraqi government, Army, and police force can take over.
No similarities at all.