Pros/cons to a dedicated area that I considered:
-You get a dedicated room where you can easily paint the trim, ceilings, walls, etc very dark.
-You can treat the room for sound by decoupling walls, ceiling, double drywall, green glue, etc.
-It is easier to control the ambient lighting
- If you entertain a lot, the open floorplan is great
- It is pretty easy not to find a high lumen projector on a budget
- It is cheaper (sound proofing a room can get costly very fast)
Only you can really answer which layout is better for your situation. I have been in your shoes and really debated between open floorplan and dedicated room, and went with open floorplan and have been happy. You have a good space in the top right for a dedicated room... So that would be tempting..