Car rental with baby seats: is it better to carry seats or rent seats?

Pros of bringing your own seat:

• no extra cost, permissions, waiting while they find the seats at the rental agency
• you know how to work the seats
• your kids are familiar with the seats
• you can also use them on the airplane

Pros of renting a seat:

• the car will be sure to have tethers
• the seats are sure to fit the car and be right for the country you're in
• the seats might already be correctly installed in the car, possibly saving time
• you will have less to carry in the airport

If I was landing late at night somewhere that I didn't speak the language, or if my children were creatures of habit who didn't sleep well in unfamiliar situations, I'd bring the seats and control my own destiny. If I wanted to use the seats on the plane (having paid for kids tickets), I'd bring the seats. If I had complicated stroller/car seat adapty combos, and wanted to use those strollers at my destination, I'd bring the seats that worked with the strollers. If I hadn't bought plane tickets for the kids, had lots of time on landing and knew that my kids accepted unfamiliar things without much complaint, I'd rent the seats for maximum convenience and bring some soft flannel blankets to make random seats more appealing to them.

I don't know how long you're renting for, but in the overall budget of a flying vacation for four people, I wouldn't let 20 or 30 Euros factor into the decision at all. I would just be trying to make the day of flying and arriving, and the day of leaving, as easy as can be, and to keep my kids content.

It depends where you are traveling from. The US and the EU use different institutes to test for road safety. If you would be bringing your EU child seat to the US or vice versa, you are legally not compliant to local rules.
I am pretty sure both type of child seat will be similar in providing a level of safety. I have heard that some renting agencies do require to use a seat that is compliant with local laws, so in that case you can end up renting a child seat, even if your brought your own.

As I currently work in a car rental agency and I have been doing so for ages, I have seen the following:
Clients child seats might not be able to be installed in all models (isofix)
If you have isofix child seats make sure that the selected vehicle has isofix bases.
Sometimes it costs quit a lot to carry your own seats on the plane, even compared to what car rental companies charge.
Big companies count on extra charges like child seats and extra driver, to increase the daily rate even 100%!
Smaller companies often provide child seats for free. So if I were you, if there is no charge for getting them on the plane and if carrying them together with all the family luggage is not an issue, I would bring my own and book the car accordingly. If I had to pay extra for the tickets, or if I had already enough luggage to worry about, I would try and find a company that offers free child seats, (ideally in very good condition and bio cleaned before the rental starts). If you choose a small you might get them for free (and installed as well).