An important benefit of having a Portuguese Residency is that you do not have to leave the country after 3 months, for every 6 month period. That is known as the Schengen rule, and it’s a pain in the butt if you don’t have an EU passport and plan to spend a lot of time in Western Europe.
There may also be certain tax and property related advantages to having Portuguese residency, but these vary by your situation, and I will not discuss them in any detail here. Do you homework, and hire yourself a good financial planner and PT lawyer who is fluent in English for that sort of stuff.
Suffice it to say that if you are a US citizen, and are planning on retiring in Portugal on just your US Social Security payments, then these will not be taxed in Portugal due to a treaty with the US on double taxation.
If you have enough of a nest egg (say by selling your home in the US) to buy a house in the Algarve, you will most likely be able to afford to living quite well as a couple on 2,000 euros a month, even if you have to pay rent — but of course better if you don’t.
Note that a Portuguese residency will also allow you to travel around in Europe on your US passport at will, and not worry about Schengen.
Also not that a PT residency will allow you to eventually access the Portuguese health care system, which is dirt cheap in comparison to the US one, unless you are on Medciare. Note there is not reciprocity with the US vis a vis Medicare. You’re on your own kid.
So if you are sick of all the drama and endless toxic horse manure that comes with living in the US, then maybe, just maybe, the peaceful, beautiful, and affordable Algarve may just be the place for you.