To be fair, Laurel has only known the truth about Oliver for what, 6 months? He's been back for almost 3 years and he's lied to her so much to protect her and his secret, so she hasn't really gotten to know the new Oliver. She gets him back from who he was, but he's also changed a lot. Felicity knows the new Oliver, and yes she has influenced him in many ways. As people have pointed out recently, she is the most human character. She is not a fighter or a soldier, so she brings that perspective to him.
But Laurel knows Oliver well enough from his past and knows who he is at his core. She was the one who believed he'd be back while Felicity was in denial that he was dead. Not to mention, when she first saw him after the island, she was pissed at what he did with Sara, but she also saw something that made her think he changed, even though he needed her to not see that yet. So I'd say she knows him better than anyone, and with them starting to team up, they're definitely going to start butting heads even more but its also going to bring them closer together.