http://Bill Tindall, E.TN
On a 3 1/2" drawer it is irrelevant using quartered lumber, or not. On such a small drawer the following is irrelevant too. In this case I would use what ever you think looks best, if looks of your drawer sides is important. Personally drawers are where my reject wood winds up. In fact this morning I sorted through my pile of shorts and pulled out all the poplar, and cherry and walnut sap which will get turned into drawer bottoms.

What makes the most sense for long term service is to make the drawer runner from something hard and durable. Maple is ideal. And, make the drawer side from something softer. The idea is that it is easier to repair a worn drawer side than the groove milled into the drawer divider or runner.

On tall drawers I use quartered lumber for the sides. I saw a slow growth poplar log now and then for this need.