In comparison, Scar never had anyone important to him to lose. He had neither a son nor a mate. All he had was his title as king... which, unlike Mufasa, he wasn't given the title at his birth. He actually had to work for it (albeit by unethical means). No one except maybe Zira and/or the hyenas respected him for that. His entire life's work, his master plan which was everything he was, was pretty much shunned by everyone else.
Sarabi still had her sisters after she lost Simba and Mufasa, but as you could see, Scar was too far removed from his own pride. He was probably closer to the hyenas than his own kind, and we know that relationship wasn't so great, either. There really wasn't anyone who Scar actually cared about, and while that means he didn't lose anyone he cared about, it also means that he never experienced what Sarabi had beforehand.
They both lost what was important to them, but Scar had much less to lose, and lost everything in the end. Sarabi definitely didn't lose everything. She was still the queen, and she still had strong relations with her pride, who she obviously worked in tandem with to keep herself up and pull through until the end. Not to mention that the Pridelanders seem to have this unifying "he lives in you" philosophy, which probably helped her to cope with her losses. Scar's only method of coping was to believe himself better than everyone else, who blamed all the problems on him.
Still think Sarabi had it worst? It pretty much all comes down to whether or not having something and losing it is worse than never having something at all.
I mean, Scar either wanted to have a family of his own, or he didn't. If he did want that, then something he did must have failed, because he didn't get what he wanted. If he didn't want a family of his own, then all he wanted was to be king, and he had to live knowing that he failed at that, too. Either way, Scar had to live with knowing that he was pretty much a total failure at everything he did—hence his narcissistic personality to cover up his true feelings about himself.