Sweden also saw a huge boom while massively raising their taxes post-WW2! And its cuts were, overall, from the highest taxes in the world, to the... 2nd-highest taxes in the world, now just barely losing out to Denmark by 1% of GDP. The correlations seem pretty complex.
In Europe, I don't see any real causal connection between tax rates and strength of the economy. If anything, there appears to be a bit of a causal connection in the opposite direction: weaker, less-developed countries have lower tax rates in order to try to lure businesses from better-developed countries. By percentage of GDP, these are the five highest-tax EU countries: Denmark, Sweden, Belgium, France, Norway. The five lowest-tax are: Lithuania, Romania, Switzerland, Latvia, Ireland.
And Germany, which has probably the strongest business sector in Europe, is towards the top; at 41% of GDP taxation, closer to Denmark's 49% than Lithuania's 21% (or the USA's 27%). Its high-tax but pro-market "social market economy" seems to be pretty successful overall.
We are smart, we are really good working, but be ready to pay a lot of taxes if you want to establish company here. While you don't need to pay bribes at least if you are doing everything legally :)
Many of the commonly-cited examples tend to pick situations which are amenable to lots of explanations. To take your example of the early US: was it low taxes and light regulation? Was it the presence of massive amounts of land and natural resources essentially free for the taking (once the natives had been suitably subdued)? Was it the jump from agrarian to industrial economy? How much of a role was played by the lack of regulation on things like owning other people and forcing them to work for you?
Similarly, it's difficult to work only from short-term examples; Ireland had a great boom, yes, but they also got a real-estate bubble and a banking crisis -- both of which are pretty clearly related in some way to the tax/regulation situation -- and that's not so great for the long-term.
It's also important to consider the historical context. Rapid industrialization has almost always resulted in massive growth, for example, but at unimaginable human cost. Whether we look at starvation and accidental and deliberate deaths as a result of a five-year plan or the Great Leap Forward, or starvation and accidental and deliberate deaths during the Western industrial revolution, we find that this growth is not always a uniformly good thing. Yet, when approaching from a framework that values only numbers like GDP, we don't see those costs.
If you want a scientific approach, you have to be considering all of these things, and more :)
Sweden, at roughly 9.5 million people, is smaller than most major US cities, let alone metropolitan areas. It simply does not have the sort of expenses that a large nation must deal with. Further, as others have noted, Sweden's industrial base was not damaged in WWII, allowing it to avoid the type of spending that most other European nations had to deal with.
Ireland's boom resulted in an even larger bust. The key driver of the boom was reduced regulations which led to rampant overspeculation by financial institutions (i.e., essentially the same thing that happened with the U.S. mortgage market).
Estonia's economic boom is the result of the discovery and exploitation of massive oil shale reserves. Unlike most oil-producing nations, Estonia is not requiring extractors to compensate, clean up, or otherwise mitigate the environmental damage.
Singapore has increased taxes several times since 2003, with minimal effects to its growing GDP. Hong Kong has also increased taxes regularly, to pay for vastly expanded government services.
One of which was the USA, which almost completely lacked taxes for the fastest period of its growth, most of the 19th century. Look up the average tax haul in relation to GDP for the US during the 19th century. The US relied heavily on tariffs instead of personal or corporate income taxes or sales taxes.
Low taxes combined with strong property rights & a strong judicial have proven to produce spectacular economic booms.
The US from 1800 to 1970, modern Singapore, and modern Hong Kong for example.
Estonia's substantial economic growth after liberalization post USSR, and ditto Ireland's big economic boom after slashing its corporate taxes (doubled their per capita income in a mere 15 years, passing Britain).
Sweden has seen a significant boom after massively cutting taxes in the last few decades.
New Zealand ditto. New Zealand boomed with their tax cutting programs:
"New Zealand went through a major program of tax reform in the 1980s. The top marginal rate of income tax was reduced from 66% to 33% (increased to 39% in April 2000, 38% in April 2009 and 33% on 1 October 2010) and corporate income tax rate from 48% to 33% (reduced to 30% in 2008 and to 28% on 1 October 2010)."