Well, Sophie answers your question in that scene itself.
Sophie: Harry Drake, he knew I wanted to be a serious actress when he signed me, but he didn't care. He didn't care about Sophie from Ann
Arbor. He only cared about Sophie from Queens. An I thought "All
right, become a star, Sophie. Then you can do whatever you want." And
now I am a star. And I still slap on a fat suit night after night
because my people don't think the audience will come see me in A
Street Car Named Desire. My people say "Stay where you are or you'll
lose everything." They don't believe in me. I wan't someone to believe
in me. To fight for me, to threaten violence for me, the way you
threatened violence for her.
Susie: Miriam & I are different, we have kind of a special thing going on, a connection.
Sophie: And I want a special thing as well. I want someone to have passion for me. Drive, vision, fearlessness. I want you.
Sophie is tired of her monotonous life & her managers who don't believe in her to try something different. She wants someone who cares for her, who isn't afraid to take bold chances & is fearless. Sophie sees that in Susie when she fights for Miriam against Sophie.