If you leave your money in the US, the advantage of remaining a US resident for tax purposes might depend on where in the EU you plan on retiring (each EU country has its own tax code with its own quirks).
In our case:
1) As US tax residents, we would pay US income tax (almost nothing based on the current tax code) and the EU VAT (only for the 6 months per year spent there). It would amount to a fairly low tax rate but, maintaining a tax residence in the US and effectively living with one foot on each continent would be more expensive (2 homes to maintain).
2) As EU tax residents (living in Europe full time), we would have to pay EU income tax + US income tax (no double taxation, but still, more hassle), plus the EU VAT, plus a wealth tax based on where my parents live. It would amount to a substantially higher tax rate for us.
Now, if we moved our money to Europe and moved our tax residence there, we would still be subjected to the EU+US income tax, VAT and wealth tax, but there are 2 advantages: 1) we would be considered expats by the US and would qualify for the expat exclusion on foreign income which means that we would pay no US income tax and 2) we could invest our money in a way that takes advantages of tax loopholes in our country of residence, hence minimizing our income tax liability. For example, dividends and interests might be taxed heavily in Europe, but real estate often has special tax exemptions. Annuities also have interesting tax advantages in some countries. So, if your income is mostly interests and dividends from your investment accounts in the US, and you are a EU resident, you might pay a lot more in taxes than if your money is invested in annuities and real estate that take full advantage of exemptions in the local tax code.
Personally, I have always arranged my portfolio to keep it "mobile", so most of my money is in taxable accounts. If you have substantial amounts of money in IRAs, you may not have that many options.