Sena, I assume the purpose of FBS is adding stabilizing proteins and, in addition, should impact crystal formation, but maybe somebody knows better.
Serum or not? Simply try it out, it's called experiment and in the end you want your cells survive the cold storage. Freeze some cells with and without FBS/FCS, continue culturing them in parallel (you probably don't want to loose your cells, just in case the frozen cells are not viable) and after one week or two, thaw one vial each and check for viability.
If you want/need to save on serum, use DMSO/FBS/medium 10/40/50. My freezing protocol with this mix is 1 day at -27 (freezer), then 1-2 days -80, then liquid nitrogen. Works perfect for all of my cells (3T3 fibroblasts, MIN6 and Ins-1 insulinomas). My protocol includes a quick and as gentle as possible handling, after trypsinizíng the cells you may suspend them directly in serum containing freezing medium, no need for the stressing wash/centrifuge procedures many people are doing. (Serum contains lots of trypsin inhibitor).