Frontal surface area, the amount of area seen by the air as the rocket heads into it nose first. The more area, the more drag. A minimum sized square has about 1/4 more area than a minimum sized circle.
Take a D or E motor and a tube/square to fit it, and call the minimum external width 1 inch.
In a square rocket, the frontal surface area is 1 square inch (1 inch wide * 1 inch high).
In a round rocket, the frontal surface are would be 0.78 square inch (area = pi r squared; radius = 0.5).
Of course, using minimum diameter is not the driving force for design these days. Lots of rockets are bigger than their engines. In all those cases, the "extra" size could just as well be square.
There might also be a bit more drag in the instance where it was tipped while flying since the flat sides would present more area to the airflow and the fact that the airflow would go around a round tube more easily. For the same reasons square bodies might tend to weathercock more than round with the same stability factor. At least it seems these would happen -- I'm not sure yet. My coffee level hasn't risen far enough to reach my calculus center yet.
Using your 1" base for convenience, a tube, seen from the side, would always look 1" wide. A square block, seen from the side, would vary from 1" wide (as seen looking straight into the side) to sqrt(2)" wide (as seen looking straight into a corner). So, it depends on the wind direction, but the cross-section presented to the wind will be, on average, in the neighborhood of 1.2 times as much for a 1" square as it would be for a 1" circle. That, of course, leaves out any turbulence effects of the airflow in the neighborhood of the corners, etc. I'm guessing there would be some negative effects from the discontinuity of the curve at those boundaries.