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I'd say it really depends on how comfortable you feel negotiating and whether you speak Portuguese or Spanish. Big companies like Hertz and Europcar have the advantage that everything's standardized and you've got protection if something goes wrong, but they charge pretty high prices most of the time. Local ones are usually cheaper, but you gotta check the car's condition real well before you take it and make sure everything's documented, you know?
If it's your first time in Lisbon and you don't know your way around the streets, I'd go with a known company to avoid headaches.
I've rented cars in several countries and in Lisbon I ended up choosing a local one because the big companies charge you a ton for insurance and "protections" you don't need.
What nobody mentions is the deposit thing: the international companies freeze a significant amount on your credit card even if you have coverage, and if there's any minor scratch afterward they screw you over with the claims.
With a local agency I negotiated better and got a decent car without so much scary paperwork.
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