I am assuming you mean for airlines' flights from their hubs?
When flying C I prefer if they only have one counter for all the flights, as either way the lines will probably be quite short. If flying Y with no status I would prefer if the airlines had counters for specific flights, otherwise the check in lines get very, very long. However, this can be an issue at airports like CAN
, which have a very large and not intuitive check-in desks area.
I think it also depends on the purpose of the flight. I take many domestic flights (within China) 2 - 3 times per week to go visit a customer for a few hours and come back. If I could, I would use the check-in kiosks (but I can't because you need a Chinese ID