One might be correct, or both dates might be wrong! This is way out of what I usually study, so hopefully someone with more knowledge will fill in the blanks in this answer. Here’s what I do know:

There have been 3 main dates given for the Ban Chiang bronze artefacts, and hence Bronze Age civilisation in the region. Each one carries with it implications for our understanding of the region’s history.

The first was given in the 1970s. In 1972, the Applied Science Centre for Archaeology at the University of Pennsylvania Museum ran a series of thermoluminescence tests on pieces of ceramic material from Ban Chiang in Thailand. These dated the shards to between 4000 and 3000 BC. In 1974, the University of Pennsylvania and the Thai Fine Arts Department appointed Chester Gorman and Pisit Charoenwongsa to direct new excavations. Charles Higham was invited to study the faunal remains.

Gorman and Charoenwongsa collected charcoal fragments from graves and sent them for testing. In 1976, based on two of the resulting radiocarbon determinations, they reported in the journal Expedition that the early Bronze Age dated from 3600 BC, within the range suggested by the thermoluminescence tests.

This first date of 3600 to 4000 BC had important implications. For example, if the Ban Chiang dates were accurate, it meant the civilisation had independently discovered how to make bronze around 2000 years before China. In fact, it would have been the earliest Bronze Age culture in the world.

The archaeological community was split by these dates, with some accepting them (whom Helmut Loofs-Wissowa referred to as “long-daters”) and others being highly skeptical (“short-daters”, who placed the region’s entry to the Bronze Age around 500 BC).

The debate raged through the 1980s as research and excavations were carried out in other parts of Thailand. All this generally found that the initial date of 3600 BC to 4000 BC was probably far too early (on a side note, sadly, Chester Gorman passed away in 1981).

By 1983, for example, Charoenwongsa seems to have postulated a new date for the region entering the Bronze Age, based on dating of artefacts from other Thai sites such as Non Chai and Non Nok Tha. The date suggested was around 2000 BC.

This date, though much later than the first, was still controversial for many reasons. For example, in 1988, James Muhly wrote

In all other corners of the Bronze Age world - China, Mesopotamia, Anatolia, the Aegean, and central Europe - we find the introduction of bronze metallurgy associated with a complex of social, political, and economic developments that mark the 'rise of the state'. Only in Southeast Asia, especially in Thailand and Vietnam, do these developments seem to be missing, and explaining (or eliminating) this anomalous situation is one of the major challenges of archaeological and archaeometallurgical research during the next decade.

In other words, it was thought that the development of bronze metallurgy went hand in hand with other developments that seemed to be absent in Ban Chiang.

Meanwhile, a fresh round of excavations was also carried out on Ban Chiang, spearheaded by Joyce White, then a graduate student at the University of Pennsylvania. In 2009, in the Journal of World History with Elizabeth Hamilton, she dated Ban Chiang’s entry to the Bronze Age to 2000-1800 BC.

Incidentally, White and Hamilton are now, respectively, Executive Director and Archaeometallurgist/Data Manager of the Institute for Southeast Asian Archaeology, which I guess explains the institute's support for the 2000 BC date.

Anyway, in 2009, (and even, as far as I'm aware, today), there was no evidence of an early experimental metalworking phase in Thailand which could indicate that the civilisation was independently developing bronze working. So the knowledge of bronze metallurgy had to have been transmitted by a civilisation outside Southeast Asia.

It was commonly thought that bronze metallurgy had been transmitted to Southeast Asia from China, yet White and Hamilton’s date preceded the date at which it was thought that China had developed bronze metallurgy. So White and Hamilton proposed an alternative theory - that bronze metallurgy could have been transmitted from Altai, some 2,500km away.

Meanwhile, Charles Higham, the guy who had been invited to study Ban Chiang’s faunal remains in 1974, proposed a third date. After Ban Chiang he had continued to study sites in the surrounding area, and in 2002 he had begun to study Ban Non Wat, just 280km southwest of Ban Chiang. He studied 76 radiocarbon dates from this site, mostly from shells placed as ritual offerings with the dead. He proposed that Bronze Age transition in the area had taken place at around 1000 BC.

He postulated that the initial date of 3600 BC could have come about because the charcoal tested had been created through the heating of old wood. Thus, the radiocarbon dating dated not just the carbon created when the charcoal was formed, but also the carbon that the old wood had acquired during its lifetime. He also suggested that looting or some other activity had moved the charcoal sample up or down in the stratigraphic profile. He noted that in several instances, the charcoal's age did not seem to match the age of the cultural artefacts found on the same layer.

He also criticised White and Hamilton’s theory, pointing out that China is between Altai and Ban Chiang, so how could bronze working have skipped China on the way to Ban Chiang? He also found fault with their dating methodology. For example, he pointed out that the pretreatment that White used has been shown to yield inaccurate results. He also pointed out that radiocarbon dating of pottery is tricky because there are so many ways carbon of different ages could have been incorporated - soot from firing, carbon inherent in the clay, even the age of wood used for firing could affect results.

Higham thought his son had figured out a way to prove his theory in 2009. In his words,

Tom spent Christmas with us in New Zealand. I thank my good fortune that one of my sons is a radiocarbon-dating specialist and Professor of Archaeological Science at Oxford. I pointed out to Tom this impossible equation [White and Hamilton’s theory], and resulting dilemma. ‘Well Dad,’ he responded, ‘have you any animal bones from Ban Chiang?’

As it turned out, he did have some pig bones that he had taken from Ban Chiang over 35 years previously. Tom Higham, his son, took the pig bones to Oxford for testing. Tom also managed to find someone who had analysed human bones from Ban Chiang. Charles Higham managed to acquire permission to carry out radiocarbon dating on the collagen in the human bones. Father and son considered this to be more accurate than testing pottery. When the results came back, they all dated the bones to around 1000 BC.

So which date is most credible? Unfortunately I am not familiar with the latest on Ban Chiang; my knowledge of the debate ends in 2010. To the best of my knowledge, the first date of 3600 BC seems to have been discredited. However I do not know whether there is as yet any consensus on the 2000-1800 BC vs 1000 BC debate.

Edit: So it seems the jury is still out on the two dates. One school of thought is the Long Chronological Model (LCM), which assumes bronze working was transmitted to Thailand in 2000 BC but was adopted extremely slowly over a period of 1,500 years, until the region entered the Iron Age in 500 BC. The other is the Short Chronological Model (SCM), which assumes that bronze working was transmitted to Thailand from southern China around 1200 BC, was rapidly adopted and accompanied by various forms of innovation, and then the region rapidly entered the Iron Age in 500 BC. From what I can gather, the SCM is more widely accepted but, as I say, this is not my area of expertise and hope someone more knowledgeable can weigh in.

Higham, C. (2012) The Dating Game and the Saga of Ban Chiang. World Archaeology Issue 52.

Higham, C., Higham, T., Ciarla, R., Douka, K., Kijngam, A., & Rispoli, F. (2011). The Origins of the Bronze Age of Southeast Asia. Journal of World Prehistory, 24(4), 227-274.

White, J., & Hamilton, E. (2009). The Transmission of Early Bronze Technology to Thailand: New Perspectives. Journal of World Prehistory, 22(4), 357-397.

Bayard, D., & Charoenwongsa, P. (1983). The Development of Metallurgy in Southeast Asia: Reply to Loofs-Wissowa. Journal of Southeast Asian Studies, 14(1), 12-17.

Loofs-Wissowa, H. (1983). The Development and Spread of Metallurgy in Southeast Asia: A Review of the Present Evidence. Journal of Southeast Asian Studies, 14(1), 1-11.

Charoenwongsa, P., & Bayard, D. (1983). Non Chai: New Dates on Metalworking and Trade From Northeastern Thailand. Current Anthropology, 24(4), 521-523.

VAN ESTERIK, P. (1973). A Preliminary Analysis of Ban Chiang Painted Pottery, Northeast Thailand. Asian Perspectives, 16(2), 174-194.