I would argue that the Tet Offensive was a tactical/operational defeat for the North Vietnamese, and a strategic loss for the US.
Ultimately, the Tet Offensive, meant to be the transition to the 3rd phase of Mao's timeline, was too early. While the North successfully moved massive amounts of men and equipment into the South to complete the offensive, they were repelled quite effectively by US and South Vietnamese troops.
In fact, the following the Tet Offensive, the Viet Cong and the North Vietnamese Army was close to decimated and near collapse due to the massive loss of manpower and political cells in the countryside of South Vietnam.
The US on the other hand, while winning this tactical victory, was plagued by cries from back home of the invasion of the South, especially after GEN Westmoreland had repeatedly reiterated to the press that we were winning the war and making good ground.
To quote William Duiker:
The Tet offensive flashed dramatically on television screens in the United States and around the world. The sight of the Viet Cong in the U.S. Embassy shook the confidence of many Americans in the prospects for final victory in South Vietnam. Media attitudes in the United States took an increasingly critical turn, and reporters stationed in Saigon sarcastically ridiculed General Westmoreland's contention that the Tet offensive had actually been a costly setback for the Communists.
Duiker continues:
In fact, Westmoreland's judgement was not that far off the mark. While U.S. claims that the attacking forces suffered over 40,000 casualties out of their total force of 80,000 may have been a slight exaggeration, estimates of over 30,000 dead, wounded and captured seem to be valid. To make matters worse, the bulk of those losses were among members of the local apparatus that the party had built up painstakingly over the years in the south.
That being said, the offensive did allow villages in the south, prior isolated from the communists by American intervention, to be placed back under the protection of the NLF.
TL;DR: The Tet offensive was a tactical defeat for the North Vietnamese because they lost a lot of man power and infrastructure in the South, however, it was a strategic victory because of how the offensive was viewed in the United States and the way it changed American's perceptions of the war.
Sources: Duiker, William. Sacred war: Nationalism and Revolution in a Divided Vietnam. Boston: McGraw Hill, 1995.
For more information on metrics during the Tet Offensive see:
Daddis, Gregory. No Sure Victory: Measuring U.S. Army Effectiveness and Progress in the Vietnam War. Oxford: Oxford University Press, 2011.
For more information on the political/strategic ramifications of the Vietnam War see:
Gaddis, John. Strategies of Containment: A Critical Appraisal of American National Security Policy During the Cold War. Oxford: Oxford University Press, 2005.
The Tet Offensive is considered a strategic victory for Vietnam (the VC was all but wiped out during Tet), because it did more than basically any other battle to sour popular American opinion on the war. Before Tet, the Army was publicly saying that the War was almost over, the VC and the NVA were on the ropes, and that it would just take a bit more to break the Vietnamese resistance. Then all the sudden, a massive guerilla uprising/NVA assault against the centers of South Vietnam proved otherwise to many Americans. There was a recurring image during Tet, of the Vietcong attacking the American Embassy in Saigon, it created a weird sort of paradox. On the one hand, you have the Army shouting that the war is almost one, yet on the other youve got communist guerrillas attack the symbol of American power in the country. Then add in that many American pundits (who were actually respected at this time) were disillusioned by Tet, and you get a large backlash against the war.
However, tactically and operationally Tet was a flop. The VC was wiped out as a guerilla force, and the NVA was badly bloodied. There was no popular uprising, as the North had hoped, and US forces were easily able to recapture any territory that the NVA decided to hold (except in Hue, where it took a bit longer. But the point still stands, the North made no territorial gains or inroads during Tet).
Whats really important to remember, is that the North shouldnt have been able to launch Tet at all. Everybody was sure (officially, it would come out later that McNamara and others in the Pentagon knew the war was unwinnable before Tet) that the North was on the ropes, and that it was soon be forced to call a cease fire. Then all the sudden, they launched a massive offensive which attacked every major population center in the South. It proved that the American government was lying to us, and it made many people question the use of the War.
Finally, its also important to remember that Nixon's "Silent Majority" regularly supported the War. When we talk about "peace protesters" or the "sit-ins" or what have you, there was this large body of people, who were never as vocal, who supported the War for most of its duration. They are sometimes forgotten, but they would completely disagree with this notion of a strategic success.