I don't think the show has ever said Tori was better then all of them. The fact that Tori always wanted approval from Jade always made me think the show and Tori never thought she was better. I'm thinking the reason why Tori got lead parts was because she was the new fresh toy and of course Sikowitz trolling Jade half the time. If anything I got the feeling the show made it Andre was the best at being a musician and Jade at singing. The show also made us believe Tori's not that great of an actor half the time.
I never got why they didn't let Liz sing. Her voice is my favorite out of everyone's. But Jade had one of the better writing out of the whole cast. Her evolution from spilling coffee on Tori to Tori Goes Platinum and Opposite Date is amazing. Actually let' be honest, Tori and Jade's friendship evolution is probably some of Dan's better writing.