Earlier quoted context omitted.
For those who don't know, that's why big and little endian were called that, because the debate was so frivolous. It's a reference to the book Gulliver's Travels by Jonathan Swift in which an island folk was split about from which end you should crack a boiled egg. (I'm a big endian for example).
Genuinely curious, what are any advantages of big endian other than "it's how we write numbers in base 10?"
Sorting (assuming your numbers are unsigned and same width, you can sort them as byte strings).
Dispatch (if only the topmost n-bits (or bytes) are needed to make a decision, that's all you need to read).