It’s purely a cosmetic concern that doesn’t actually change the way your grilled cheese tastes…right?

Technically yes, but it certainly *seems* to make a difference. And depending on the ingredients, it’s possible it does — depending on exactly how and where they’re cut, certain meats or cheese might actually taste slightly different. Unless it’s all in your head, of course, in which case it’s perfectly fine to base this decision on which shape you like better. Horizontal is the standard, but there’s just something fun and even picnic-y about diagonal sandwiches, isn’t there?