American property tax is decided at minimum by state and often by county or town, so it differs wildly.
In most places, it pays for the local education system. This actually leads to massive inequality, where richer places have better-funded schools. (There are mechanisms to correct this, of course, at the state level, but it does sharpen the differences quite acutely in places where this is true.)
In many states in the northeast, the bill can be quite high, a combination of a higher tax rate and more expensive real estate. So, for instance, if you owned a £500k house, you'd pay just shy of £13k a year in property taxes. In Alabama, on the other hand, it would be around £1500 a year.
However, while Americans have a similar average income tax rate, they tax their wealthy people far less than the British. The highest federal tax bracket is 37%, and you only get there at over £375,000/annum. If you were making the equivalent of £50k a year, which in Britain would get you to 40%, you'd be taxed at 22%. (I'm not getting into the states, which have their own rules.)
Conversely, income tax is higher for the very poor. While British people have no tax bracket until £12,500, Americans get taxed 10% on any income at all, even if people make $6000/year.
(I should say this is all for single people. Married households, you don't have to pay top tax rate of 37% until £453,000/annum, while you still have to pay 10% on all income at minimum.)
And finally, the British system has much higher VAT than American sales tax. However, while British VAT is usually zero-rated for things like food and necessities, in some American states, even basic necessities have up to a 10% sales tax added to them.
In other words, while I agree that property tax is a good, non-regressive tax, much of the rest of the American system is far more regressive than the British system.