Laurel had everything.
Dinah already had lost everything so she didn't have anything else to lose.
Dinah almost had the chance to be someone big sister, but her baby sister was dead soon as she was born, with the umbilical cord wrapped around her neck. She hated Christmas after that.
Laurel loved having a sister. It was like already having a best friend without looking for one.
Dinah always had trouble find her. It was the only thing that made her parents pay attention to her
Laurel was always the golden child compared to Sara's black sheep.
Both fell in love with Oliver Queen at the age of 7 when they first meted him
With him Dinah forget about everything going on in her life. He made her feel like a whole person. So she completely broke when the news of his death came.
Laurel tried convince herself that Oliver was a great guy and most importantly a loyal boyfriend to her.
However that illusion shattered when she found about The Gambit and her own sister betraying her. Laurel screamed until she got Laryngitis.
Dinah moved to Central City for a fresh start away. Away from the place that was no longer home because he wasn't there anymore.
Laurel stayed because Starling City was still her home and she was all her dad had left of their fractured family.
Dinah was consumed by grief.
Laurel was unsure on how to grief in her situation.
On December 11, 2013 as Dinah got into a screaming match with her latest fling when he apathetically told her that she needed to stop loving Oliver's ghost. That's when her screams killed him.
Laurel never became a Meta Human. She had become The Black Canary in honor of Sara. Still Felicity reminded her that she was Laurel not Sara.
Dinah had no one to remind her that she was still Dinah and not this Black Siren character that the media dubbed her.
Laurel died fighting and protecting for what she believed in.
Dinah didn't want to die so she accepted Zoom invitation to be part of his army and became his top lieutenant.
One became a killer against her will. The other sought a way to become a hero.
They are so opposite, and yet the same. That is the nature of Doppelgängers isn't it?