Which is safer for binge eating. topomax or vyvanse (lisdexamfetamine)?

No difference: There is no such thing as "best" or "worst" medication, only those that work and don't work, based on the patient's individual circumstances and genetics. Talk to your doctor for medication adjustment.

Both medications: are actually pretty well tolerated. I'm not aware of any significant discontinuation data(which correlates to some extent to safety or at least the presence of adverse effects) for either in regards to binge eating disorder.