Controlled residential ventilation + fireplace + kitchen exhaust, does it work?

Of course, an extractor hood also draws in odors. It does not separate them and say "ew, I’m not sucking those in." Of course, not all odors disappear. Besides the system issue, the execution is important. The exhaust hood in our former terraced house does a worse job than the recirculation hood in our current house – also with regard to odors. Everything you lead out of the house as warm air without using it has to be reheated. However, given the operating time and the volume of air you reheat, this is not really a decisive factor.

I will work with recirculation, I'm not in the mood for all the hassle with breakthrough and air box etc.
With KFBs I've heard both. Like yours, that recirculation is just as good but also that exhaust simply can't be beaten.
I don't really care. It can't get worse than it is now.
I once lived in a rental apartment for 3 years without any DH, it worked too, the food tasted good and I didn't suffocate either. However, the stove and the furniture directly next to it tend to get greasy faster. That means either cleaning more often or new cabinets/countertop every few years.

So we only have recirculation air (with activated carbon filter) and the odors in the open living kitchen area are (my personal perception) not "worse" than, for example, at my parents' who have a vented hood.

For me, the positive aspects of a recirculation hood also outweigh... The only thing a recirculation hood doesn't manage is to expel the moisture from cooking outside. But for that, you have your controlled residential ventilation...

In principle, I also tend towards recirculation. Are there any important things to watch out for with the hood?

We received 3 different devices from 3 kitchen studios:

Bosch - DFR097A52 Neff - D95IHM1S0 Falmec - Verso 85 Schwarz Glas

Can anyone say something about this? How important is the activated carbon filter? Should you only buy devices with an activated carbon filter? This is a bit off-topic, sorry for that, but maybe someone can quickly share some information here :)

Activated carbon filters "actively," so to speak. Due to its high porosity and thus large surface area, it binds substances very well (by the way, also odors) and is not given for poisoning cases without reason. I don't know if a cellulose or even plastic filter works equally well. Unfortunately, I can't say anything about the hoods (except that Siemens, Bosch, and Neff are basically the same manufacturer - for kitchen appliances).

Activated carbon filters so to speak "actively." Due to its strong porosity and therefore large surface area, it binds substances very well (by the way, also odors) and is not given for poisoning cases without reason. I don't know if a cellulose or even plastic filter does the same. Unfortunately, I can't say anything about the hoods (except that Siemens Bosch and Neff are basically the same manufacturer - for kitchen appliances).

Thanks already for the info!

I just think that if we decide on the recirculation hood, it is all the more important to choose the best hood for us and certainly invest a few euros more.