Sometimes it's the nipple size or shape. Sometimes it's the difference in letdown/milk delivery speed.
Sometimes the baby just prefers one side, maybe b/c of how they were lying in utero? They like having one cheek down, one up. Start on the preferred side for a few mins, then *without flipping her body around* slide her over to the other side, so she ends up in the football hold on that side. Make sure and use pillows for comfort.
If it's letdown that is too fast, try lying down for nursing. Or nurse in a semi-reclined psosition, so the milk has to go "uphill."