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Bigger than what ? Smaller than what ? If you have a certain perimeter and you want to cram the most area inside it, or if you have a certain area and you want to enclose it in the shortest perimeter, then you must make the perimeter circular. If you have only a limited number of fence posts and a circular perimeter isn't practical, then you make the perimeter square.
You cannot really compare whether the area or perimeter is bigger, since they have different units. If you want to compare which one is numerically bigger, that depends primarily on what units you are using, as well as the magnitude of the lengths.
units with perimeter square units with area
Different polygons have different relationships between perimeter and area. For example, if we assume regular polygons, an equilateral triangle and a square have different perimeters for the same area. If you allow irregular polygons, the variety is even bigger.