Dual Citizen (US and Germany) here. FATCA used to be a huge problem in the EU, but by now most banks have returned to accepting US citizens as customers. You need to file two tax returns, though (and a report on foreign bank accounts).
As a general rule, due to generally higher taxes and social security contributions, net wages in the EU are somewhat more evenly distributed, with high earners earning less than they would in the US and vice versa. From a stash building standpoint this might be disadvantageous. OTOH, in case something goes wrong (injury, illness), you’re affordably covered.
On your follow-up question: I don’t know the situation in most countries, but post-FIRE, be wary of countries with wealth tax (e.g., France, Spain, possibly Netherlands?).