Living room = carpet
Wood floors are a fashion thing, and will come and go as do flared trousers. Traditionally carpet was the thing to have as it can be expensive to make and so only those who could afford it would cover a wood floor with a textile. A wood floor being something a stage above pounded earth. A living room is somewhere you would take guests so would show it off there. An equivalent of having a BMW on the drive.
In reality we mostly have tiled (kitchen/diner) or wood. The living room and daughters bedroom are only rooms that are carpeted (living replaced only a week ago). Did consider wood but after talking to one of our neighbours that did it last year decided against it as they went off it due to noise and that it isn't very nice to sit or lay on without going numb.
Depends on your room. A large one in a modern house may invite 'strictly come dancing' comments, a small one in a victorian terrace with a rug and original floorboards would suit it admirably.
I voted carpet, but its
your home so whatever you choose will be right.