hard to give real evidence, because binary has few feats. to me it just stands to reason -- she gets powers from a white hole. ss can easily make white holes -- theoretically he travels through them when he dimension travels or goes into hyperspace. if he wanted, he could always just seal off the hole and steal the source of her power. but, he likely wouldn't have to. see controls stellar energy -- that's energy that ss can literally swim in unaffected. ss obviously has FAR greater versatility with power cosmic. she can put out a lot of energy, but ss can handle whatever she's got pretty easily -- if he even let's her hit him. speed is another huge advantage he has. he has a lot of ways available to beat her.
against common opponents is another gauge -- quasar beat her easily. ss has given him fits in the past and thy battle to draws. gladiator also ko'd her. ss could kill glads easily by using the right radiation and when they did fight (out of continuity) they again battled to something like a draw.
based on versatility, skill and speed, i see ss beating her every time.