Is it generally better to cut chicken breast with or against the grain?
Alton Brown talked about this on an episode of Good Eats, and here's what I remember:

If you cut with the grain, you'll end up with long strands of protein, like this:

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From what I understand, this means that it'll be pretty chewy.  Your mouth has to work harder to break the strands up into smaller pieces to be more easily swallowed.

If you cut against the grain, you get strands like this:

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You can see that the strands are much shorter, which means the meat will fall apart more easily (each strand doesn't have as much surface area to connect to adjacent strands) and will therefore be more tender.