I am a US citizen, just in my second month in Ireland. But, here is what I have found so far, having studied while considering whether to come here, and talking with colleagues from around Europe:
I think FIRE is more difficult in Europe than the US, because the general higher level of government involvement in personal affairs is geared toward traditional retirement age. Since FIRE is, to a great extent, conducting yourself contrary to the norm, you have more to fight against. That said, it is also important to understand where you would likely retire to, as earning money in one country, but living in another, can be fraught with tax consequences you have to consider. I don't think there are really any surprises here.
Factors in favor of FIRE in the US:
Tax level, particularly capital gains tax
Investing costs and availability
Factors in favor of FIRE in Europe:
Public health care system
Public pension system
So, specifically for Ireland, which is the extent I have really examined so far:
Income tax rate is 20% up to euro 34,500 singles / 43,550 married couples. 40% after that.
Capital gains rate 33%--so, penalty on low earners (in effect, discourages investment) but while high, still better than income tax for high earners
Penalty interest level of 50% on savings, as a result of a 2008-era law still in place. They call this DIRT. You can guess the attitude on large amounts of savings.
Our company's defined contribution plan (equivalent of a 401k) is run by an insurance company, as they all are. No Fidelity / Schwab here. The low cost index funds are .6% per year.
Funds from the pension are available at 65, with some limited provision for access at early retirement, as early as 50.
Trading fees to buy or sell a stock in Ireland is 1%. Not that there is a lot listed here; it seems Schwab is very popular, as they support the extra paperwork for foreign ownership, and allow access to US funds. There are a lot of "discount brokers" out of the Netherlands, too.
I don't plan on staying the 10 years needed for an Irish public pension. However, due to the tax treaty with the US, my public pension taxes aren't lost--they will give some contribution to my Social Security payment, in lieu of years worked in the US. Ironically, it will be less than if I had worked in the US...
The obvious worry in the US is covering healthcare before Medicare. While Ireland has a public healthcare system, there is a vibrant private system working alongside it. While the public healthcare is good, the commonly observed issues with such a system exist: long waits for specialists, patients held in the hallway in overcrowded hospitals, etc. But better than trying to live without in the US, or something you can't even afford to use because of the deductible. If you were going to retire to this, you will need to have established some work history--the Irish government is skeptical of people just retiring here.
As I said, I have talked with a number of colleagues from other European countries, who also have differentials / blended situations to work out--there is free movement of labor, but that doesn't mean there are no disconnects. It seems that while the details may be different, the general trend is the same: the caretaker government steers you toward an "on time" retirement and support in old age, although there is pressure to increase that due to costs. But the cost of doing that, high taxes, particularly on passive income (relative to the US situation) means that the impact of your Mustachian ways is blunted somewhat. I think this is also shown by the very limited number of FIRE blogs I have found from European voices, although that could be a matter of interest or even awareness, too.