What's the appeal of a circular watch other than the fact that it's traditional?
Tradition is a pretty big appeal.
Heck, look at the Apple Watch for proof of that. They went with an overwhelmingly watch-like shape (square version), straps, name, even a crown, in an attempt to evoke nostalgic jewelry feelings.
Wrists are rectangular when viewed from above. Seems circular watches are just pocket watches you can wear on your wrist, and pocket watches got their form from necessity (gears).
Pocketwatches are flat rounded shapes so they can more easily fit in and out of pockets.
As far as round for clocks in general, it's because time is based on rotation, after all. From sundials to clocks that follow the orbits of planets and the moonphases, it's all about going around and around
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One consideration is that square watches can't be made resistant to underwater pressure anywhere near as deep as round watches can.
Moreover, you cannot put a rotating diver's timing bezel, or a pilot's rotating E6B slide rule on a square face.
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I would say that round makes the most sense for a clock face, because then the hands and the markings are always equidistant.
Conversely, text makes more sense in a rectangular display.
So I propose that they should be combined. Use the full circular display just for round watchfaces, and the interior square part for text apps.
For example, because of its large bezels, an Apple Watch sized text display could fit inside the Moto 360 display:
So a future Apple Watch could be round for watchfaces, but just use the interior for legacy apps.