[[ ]] are equal to test keyword.
You can also use [ ] but [[ ]] isn't compatible with all shell types
To me, if I understand the real sense of question, question itself isn't well-formulated.
Those brackets have to be here not so much for order determination, but because the bash synopsis require them
Edit
Question is changed, so my answer too.
[[ ]] is used against [ ] because you don't have to worry about quoting the left hand side of the test that will be read as a variable.
Moreover, < and > doesn't need to be escaped
