American expats in the UK usually say it's expensive. British expats in the US also say it's expensive. I've looked at the numbers, and comparisons are difficult. We've had to learn entirely different ways of budgeting and looking at money.
I'll leave out healthcare, since 1) we all know that's more here and 2) the actual numbers are incredibly variable (I know people who get 100% of their premium paid, and people who get less than half). As I said above you absolutely must calculate the benefits including health cover when considering an offer.
Housing is a very tricky comparison because it's so local. Many American expats are in or around London where housing prices are high--and they think it's even more expensive because of what you get for the money. Similarly Brits who come specifically for jobs are often in the highest cost cities. Americans come to the UK expecting a more American kind of lifestyle and are shocked at what it costs there.
Taxes are calculated differently in both countries and this can lead to unpleasant surprises. US has much lower national income tax, but can have much higher local (state and property) taxes. Texas, for example, is known for high property taxes because they don't have state income tax and our property tax goes to fund schools. (In New York and New Jersey, both sets of taxes are very high. Then I found out what teaching wages are there....) Here in Maryland, I pay less property tax, but we have state income tax.
HOAs are their own question and they can provide amenities--it's not a required cost unless you buy a condo, which will always have some type of association fee.
Utilities: Even if the price per kW/hr or therm was the same, you'll likely use more electricity and gas here unless you are living in an apartment or a very mild climate. Houses are bigger and the climate is more extreme. People sometimes come to the US and say "ooh the houses are so nice and big!" but you need to heat and cool them, and in a lot of the country, air-conditioning is a necessity rather than a luxury.
Cars and petrol are cheaper--but if you're not somewhere like SF or NYC, you've got two cars, and you're likely driving more, and your car gets lower mileage, and so even though the petrol costs less per litre there goes your total cost.
Groceries are a mixed bag as prices have gone up noticeably in the US since we have lived here. I did some online comparison shopping not long ago, and some things are cheaper here and some in the UK, but when you move countries there is a period of having to learn how to shop again and adjust your shopping habits to what is available there.
Internet is more expensive, period (the USA has become one of the most expensive countries).
Doctors are generally paid more here, but the variation between specialties is much higher. Family practitioners (GPs) are not paid that much more than UK GPs and their training costs much more.