The nature of a coffee table is such that it tends to define a space. It carves the room up into pathways, that then forces people to travel left or right, along or aside the table itself. It is the spine of the living room, and at the same time, it defines the nature of interactions in a space. Conversations will occur across its surface, games will be played, and the overall nature of the room will be defined by its presence.
When selecting the shape of the table it's important to be guided by the inherent shape of the room. If the space features a lot of curves, you will want a table that will flow with those curves. On the other hand, a more straight lined contemporary space would be better suited to a boxier design.
Small Coffe Tables
Another thing to consider is space limitations. A round or oval table will always take up less space than a similarly sized square or rectangle. This is because the curve means that there are no corners jutting out into the space. However a squared off table means that the piece can be butted into a right angled corner, allowing you to save some room that way.
Another element to consider is the stylistic nature of round versus square tables. A square table is often considered to be more modern and contemporary, fitting into the machine age with a precise precision that matches the industrial nature of our times. By contrast the softly flowing curves of a rounder table will tend to evoke ideas of a more classic look.
The difference between a round and a square coffee table will involve ideas of both style and space. It's important to understand the nature of the room, and the purpose of the table, before actually going out and selecting a piece.