I work a lot with embedded, and in particular files and memory dumps from embedded systems. In my experience, it doesn't matter that much if you are running on one or the other, what matters is if you are working with files/data from the other one. Almost all files/dumps/structures/whatever have some magic number header where we just do something like
var val = reader.ReadUInt32();
if(val == 0xAABBCCDD)
reader.SwitchEndianess = false;
else if(val == 0xDDCCBBAA)
reader.SwitchEndianess = true;
throw new InvalidDataException();
I suppose it could matter if you try to write a file with a defined byte order though.
Also, many processors have runtime switchable endianess, including most ARMs if I'm not mistaken.