The rectangular tables are the most common, which shows that they are a practical, functional and comfortable option. They are perfect for elongated dining rooms and they allow for more diners in less space. In a small room, a rectangular table can be shoved against the wall and still be perfectly practical.
If you have one formal and one casual dining space, you can really go to town with different chair designs for both. A casual spot will do best with sociable, comfy seating that naturally leads to conversation, whereas a formal setting is where you can play around with luxury fabrics. If you only have one dining room, you're going to need to combine all of these elements in one set of chairs, if possible!