I'm no Home Theater expert, but I have pretty simple standards and tastes. As long as the living room is a nice universal, comfortable place for other people to hang out with me, the TV doesn't have to be super big. Personally, I'd always prefer a theater room.
As far as I'm concerned a theater room doesn't necessarily mean Projector. I don't have a dedicated room yet, but I may be looking into a 3 bedroom apartment for one soon enough, hopefully this time next year. My theater room would likely be extremely small, a guest room, no bigger. It would be well insulated and sound proofed, providing some decent acoustics. Wall mount a 75-82 inch TV, say about 10-15 ft viewing distance, that means full HDR compatibility, and maybe a singular leather reclining couch. Surround wired, with perhaps some custom cut blackout curtains lining the walls for cleanliness and design. A dedicated 4K player and at LEAST a 5.1 sound system(but 7.1 or atmos could be entirely possible). This is the room where I'd store all of my movies and games, leaving some nice space in the living room.
I'd install some remote control wall light sconces with dimming, maybe some atmospheric lighting around the bottom of the couch, some subtle bias lighting behind the TV if necessary, some nicely framed movie posters, and you're pretty much good to go. I would only ever have to accommodate MAYBE 3-4 people at a time, max, so a singular couch would do the trick, or 4 separate matching recliners(depending on shape of the room, if it's more rectangular or square). It's just my Girlfriend and I for the foreseeable future, so I wouldn't need anything highly expensive or extravagant, just something atmospheric, comfortable and enveloping. A place to escape into for a few hours.
On a budget, I can likely accomplish this for under or around 3,000 bucks. That's not too bad in my mind. That way I can have the best of both worlds, a nice open living room, simplistic decoration and design that I can leave my girlfriend to handle much of, with a decent 55" TV with cable. A game room (which We've had for the past 6 years), with retro game consoles a CRT TV and my old 43" Plasma with good ole component connections. The bedroom with a cheap 23" for night time decompression, and a stylish, yet simple dedicated theater room with a 75"-82". Say, TCL 6 - 8 series for a nice budget, good performance TV. Though I'd ultimately love to have a curved TV in there, those are becoming extinct sadly. My dream would be a curved 82 incher for my theater room, but not likely to happen.
I obviously wouldn't be against a projector, but I gotta have that full, beautiful HDR brightness, so I'd lean more into a TV. It's just a lot more versatile, especially for the much smaller room that'd I'd have.