I disagree. Sara fits the first type when on Arrow in season 2 as well not just now when she's on LOT.
Sara became stronger as well after what she endured and I thought Laurel was an annoying character.
Sara was still going through her crucible in season 2. She felt guilt for what she had done, and she was still killing her enemies. Her and Oliver used each other to escape the pain they were both going through. Like Felicity said to Laurel in season 3 "I think Sara wore her mask just as much to hide her demons as she did to help people, and i dont see that with you. You have a light inside of you that Sara never had, so maybe you should stop trying to be Sara, and just be yourself". That is a nice way of summing up the differences between them in season 2. Laurel wanted to help people simply because it was the right thing to do, even before she became BC, wheareas Sara did most of what she did to escape the pain.
The following conversation happened in the 2nd last episode of season 2, where she even admit that she is not a hero.
Sara: You don't know, Laurel, about me. About who I am, and who I've become.
Laurel: I know you're a hero.
Sara Lance: I'm not a hero... Laurel. I'm the furthest thing from it. I am "Ta-er Sah-fer." That was my new name. Because of the woman that I was, the girl that I was, was gone.
Laurel: I'm not going to pretend that I've been through anything that you have. But one thing that I've learned in the past year is that these things... they don't break us. They make us who we are.
Sara: And what I am... is irredeemable.
Laurel: What was that word you said before?
Sara: Ta-er Sah-fer.
Laurel: What does that mean?
Sara: It means "The Canary".
Laurel: If you're so far gone and so irredeemable... then why would they know you by such a beautiful name?
This conversation was the beginning of her trying to redeem herself and becoming a hero. Laurel, like she does with pretty much everyone, saw the best in her and forgave her, just as she did with Oliver after what he did to her when he cheated on her with Sara, and her father Quentin, who used her as bait to capture the hood. Heck, she even worried about Malcolm's safety in the episode Dark Waters this season, despite everything that Malcolm had done to her (ie he killed Tommy and her sister).
In a similar manner to Felicity and Team Arrow being Oliver's light, Laurel was Sara's light. She saw the best in her and brought out the best in her, and sent her on her way to becoming a hero. Right after that, Sara risked herself to save a kid from a fire. After that, it was not all smooth sailing of course. Sara then, in a similar manner to Oliver in season 3, felt that "the ends justify the means" and re-joined the LOA because she felt that it was necessary to stop Slade (they would only show up and fight Slade and his men if she re-joined them). Like Oliver in season 3, she believed that you had to do desperate things to stop powerful enemies like Slade or Ra's. She re-joined them in order to save Starling city, not because it was something that she wanted to do. She was not a hero yet, but she was on the right path, although she still had a long way to go.
After she was killed and then brought back by Laurel, she returned with a blood lust and a need to kill as a result of the Lazarus pits. Perhaps, in different circumstances, she would have given in. But once again, she had Laurel who was there for her and who wanted to help and inspire her.
Sara: Laurel, i died. I am still picking up those pieces. The Lazarus pit brought me back, but it left me with this need to take. To kill. I'm dangerous.
Laurel: After you died, I needed a channel for my grief. I found it in becoming the Black Canary. I found it in you.
Sara: For me, being the Canary was never that positive.
Laurel: Then don't be the Canary. Do what Oliver's been doing. Do what this Rip Hunter is offering you the chance to do and... be a hero in the light. Be the White Canary.
Sara: [Laurel shows her the White Canary costume] Where did you get this?
Laurel: I have a resourceful friend named Cisco.
Sara: Where's the mask?
Laurel: You don't need it anymore. You've lived in the shadows long enough.
They both inspire each other, but it is Laurel who inspired Sara to become more heroic. Laurel was always heroic and trying to save people, even before she put on a mask. It was Sara who inspired her to take it to the next level. Laurel became the Black Canary because of the grief and pain Sara's death caused her (black, of course, being the colour mostly asociated with grief, mourning and death, and she kept the Canary name to honour Sara). Initially she wanted to avenge Sara, but then decided she wanted to honour her and make sure that she wasn't forgotten.
Of course, Laurel eventually decided to forge her own path after Felicity suggested this to her "I think Sara wore her mask just as much to hide her demons as she did to help people, and i dont see that with you. You have a light inside of you that Sara never had, so maybe you should stop trying to be Sara, and just be yourself". Even so, Sara was still the reason she became BC and put on the costume, even if her motivations changed, and her sole reason was not just Sara anymore. Sara still inspired her to become BC in the first place, through her death.
Sara became the White Canary, because she was inpired by Laurel's light and hope. She wanted to make up for her past in the LOA and fight the bloodlust that the lazarus pits gave her. She wanted to become a "hero in the light", because of her sister.
Ultimately, who the better, more interesting or more annoying character is, is subjective. But Sara did not fit the first type of person going into a crucible "The ones who become stronger from the experience and survive it
" in season 2, rather the third type "the ones who learn to love the fire and choose to stay in their crucible because it's easier to embrace the pain when it's all you know anymore". What she said in her conversation with Laurel when she said she is "the furthest thing from a hero" and "irredeemable" confirms this. She was allowing the guilt to overcome her, rather than trying to fight it. She was not as far gone as the likes of Slade or Malcolm though.
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