##They're synonymous. Use either.##

I wracked my brain to think of a time when you would use "side to side" but not "to and fro" but I couldn't come up with one.

##They're synonymous in your example but "To and Fro" allows for more variety of movement.##

Jason points out in the comment that "to and fro" means movement an (any) opposite directions, not just side to side. It also relates to moving between two locations.