The main difference between Shadow and Sonic is that Shadow is very emotional, but Sonic is not. Shadow is incredibly open with what he's feeling, telling the world how much pain he's in, but Sonic locks all his emotions away, including the pain. Heck, one of the lyrics in "Find Your Flame" is, word-for-word, "I can bury the pain". Shadow faces his problems head-on, while Sonic's whole mentality, as evidenced in 06, is to run from them. Shadow is slowly healing from the pain of loosing Maria. Sonic may seem fine, but the cracks show. He's become increasingly violent towards Zavok after the war and metal virus, as shown by him snapping the neck of the Phantom copy in the boss fight in Forces and verbally hoping that the zeti was miserable in Frontiers. In Sonic Battle, Sonic copes with Emerl's death by pretending he's joined the chaos emeralds. While Sonic and Shadow both need therapy, I think it's obvious who needs it more.