Nope. The 38mm rectangular display fits perfectly inside a round 42mm watch with the frame bezel Jony Ive imposed on it (there's no reason why the display can't go all the way to the edge).
Here's some photoshop mockups I did 1:1. The first is the watch with the usable display area delineated. Note the slight reduction of the 38mm inside the 42mm. Keep in mind Ive chose not to have the image extend under the curved portion of the crystal. The display could absolutely extend to the edge.
http://www.newyorker.com/magazine/2015/02/23/shape-things-come
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Now we have the round watch overlayed on the Watch, making it only slightly wider, but then slimmer at the top and bottom. Note the inset 42mm display fits perfectly inside the case of the circle. And if Apple chose a flat crystal, they could use all of that space -- remember Ive chose not to extend the display to the edge. But let's stick with Apple's current design, and assume the only space we have is equivalent to the 38mm display including a border.
http://www.newyorker.com/magazine/2015/02/23/shape-things-come
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So now we have a typical text use overlaid on the round shape as it would appear on the 38mm watch.
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But look at this -- in the rectangular shape the Name of the contact and time take up room at the top of the text view. But look what happens when that information is moved to the unused spare areas of the round circle. Now there's not only more information, displayed in the text window, but it can also be enlarged back up to the same size the 42mm watch would have displayed it -- and that's assuming we're stuck with the border. Since we aren't, the 38mm text box doesn't have to be any smaller than it presently is. And, Apple isn't constrained by these sizes. I wouldn't be surprised if they offer a 34mm, or 36mm version to fit more petite wrists, without substantial loss to legibility.
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I'm absolutely satisfied that there's absolutely no compromise between presenting text on a rectangle vs. a round watch. In fact, you can have even more text on a round watch, and more information impossible on the Watch without restricting displayed text. And frankly, most of the screen shots I've seen from Apple's apps (aside from straight text) would translate better on a round screen than a square.
The difference between Moto 360 and the Watch boils down to design implementation, and nothing else. Apple would blow this concept out of the water.