I "think" another way to ask your question is what is the difference between a dipole array and a slot array. A dipole array is an array of discontinuous metallic elements. A slot array is a continuous metal sheet with the elements cut out of the sheet. If the element shapes are the same, the slot and dipole arrays have almost the exact opposite frequency response.
I think what you are calling "patch-type" is what I am calling "dipole arrays," and what you are calling "aperture-type" is what I am calling "slot arrays."
The patch type FSS is used where transmission is minimum at resonating frequency i.e. reflection is maximum. Below and above the resonating frequency, transmission gradually increases and finally reaches its maximum value. Reverse situation arises for aperture type frequency selective surfaces. Here transmission is maximum at resonating frequency i.e. reflection is minimum. Below and above the resonating frequency, transmitted electric field gradually decreases and finally becomes zero.